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Hej,
if you derive the advection equation with respect to t you get
u_tt=-a*(u_x)_t=-a*(u_t)_x=-a*(-a*u_x)_x=a^2*u_xx
Thanks a lot!
Hi,
I have a question concerning exercise 14 part b, and more specifically the part we should derive a condition relating sigma and vita.
Should we take into account the third term of the sinusTaylorexpansion or just assume sin(ksi*Dx)~ksi*Dx ?
Thanks, Michail.
Hi,
it is sufficient to only take into accoutn ksi*Dx for sin(ksi*Dx).
Philipp
An alternative way to show that u_tt=a^2 u_xx is:
do the derivative of u_t+au_x=0 with respect to x, and then with respect to t. Then, you will get in each a equation a term u_xt and u_tx which are the same due to the symmetry of secondary derivatives. Eliminating thus this terms gives the u_tt=a^2 u_xx.
But of course the above derivation is equivalent.
Philipp
Hi,
I have a question about the definition "ABSOLUTE STABILITY" of a scheme. Does it mean:
a) the scheme is stable when the analytical solution is stable or
b) the scheme is always stable, even if the analytical solution is unstable?
Besides that, if I say "the scheme is "UNCONDITIONALLY STABLE", is this statement equivalent to "the scheme is ABSOLUTE STABLE"?
Hello,
there is one question conserning question 29 (b). Which type of discontinuity is excuded and why? Is it discontinuity of entropy over the shock? Why can we exclude it? We have done the same in the simulation of the shocktube (home work 4), did we neglect something?
Concerning the question about absolute stability:
A scheme is absolutely stable if the complete left half-plane is stable (i.e. included in the region of absolute stability of the scheme). This corresponds to your option a).
For the term "unconditionally stable" I guess there are various interpretations possible. My definition would be that unconditionally stable would be much stronger, i.e. including the complete plane (corresponding to your option b) ).
Philipp
Concerning the shock tube:
In question 29, we assume the isentropic Euler equations, which is the same as in HW4 (leading to weak shocks). The full Euler equations would have one equation (energy equation) more, i.e. three components. Therefore, we would also get three different characteristics instead of only two as in the example (see notes Lecture10.pdf page 6). The additional feature absent in the isentropic case is the "contact discontinuity", characterised by the same pressure but different densities. The reason for this discontinuity is that it separates regions that have been processed by the shock on the right and by the expansion fan on the left, which leaves the two regions on different entropy levels. However, if these are not allowed due to an isentropy condition, this discontinuity disappear.
Philipp
One question to number 28:
Is there a mathematical difference between the terms "physical" and "numerical" boundary conditions? Or is the difference just the reason why they are needed, e.g. the relation to the number of ingoing characteristics?
Tack.
What we call "physical" boundary conditions are the ones that are needed to solve the physical (or mathematical) problem. For instance that means that in situations where we solve the advection equation and we have outflow, then no physical condition is allowed.
Numerical conditions are not needed from the mathematical/physical point of view, i.e. specifying them would render the system ill posed. These are needed for certain (e.g. central) discretisation schemes and must be obtained via extrapolation from the inside.
Philipp
I have some doubts about the question 26:
- The linearisation I did for the barotropic gas dynamic equation give the correct result except the denominator of the last equation:
\(u_t+a^2/(\rho_0+\rho') \rho_x\)
to get rid the last rho' we have to suppose that it is negligible compared to rho_0?
- Moreover I found that this system is hyperbolic with characteristics =+-a
However I do not get what does it mean characteristic variables thus the characteristic formulation we have to write there.
- Another question is, how much deep we have to go for the last questions? The answer for some of them is the entire topic of 1 lecture, I want to know, if it is possible, if we have to write every steps or a summary is sufficient.
Thank you
Fabio
I also spent hours with this question 26. The trick is to write the system in the linear form q_t+A*q_x=0, where q is the vector with conservative quantities rho and u.
Then you can diagionalize A=V*L*Vinv (L is diagional matrix with eigenvalues, and V is matrix whose columns are eigenvectors of A), so your system can be written as Vinv*q_t+L*Vinv*q_x=0. This becomes decoupled system with characteristic variables: w_t+L*w_x=0, where characteristic variable is w=Vinv*q. Further you can solve the system analyticaly for w=w_0 (x-lamda*t), and obtain q as V*w.
I hope this helps.
Hej Slobodan
Really thank you for the answer!!! I get your point and i is a very smart way to find the solution...however I get \((\rho-u;\rho/a*(\rho+u))\) as characteristic variables, I hope you have the same:)
The only thing is that I have a different result for the task e but I have to check it now...I think I made some mistakes:)
thank you again for the help!
I think the result I posted is wrong...
Hi,
regarding question 26: Indeed, you start with the variables in *primitive* variables, i.e. $(\rho, u)^T$. To then get to the characteristic variables, the idea is to diagonalise the matrix, as Slobodan writes above, this gives you the eigenvalues and eigenvectors, and with that the rule to transform the state variables into $Vinv*q$, which are called characteristic variables. In fact, the characteristic variables are also called Riemann invariants. In case of a linear problem, the eigenvalues are independent of the solution (for instance $a$ is independent of the solution $\rho$ or $u$), then the two equations are completely uncoupled and can be solved independently. In the general case, the characteristics speeds are only valid close to the point under consideration, but in general the two equations are still coupled (through the eigenvalue).
Hope this helps,
Philipp
Hi Fabio,
To get the second equation correctly you need to expand the term
\(\frac{a^2}{(\rho_0+\rho')}}\)
in following way:
\(\frac{a^2}{(\rho_0+\rho')}(\rho_0+\rho')_x\approx\\ a^2 (\frac{1}{\rho_0}-\frac{\rho'}{\rho_0^2})[(\rho_0)_x+\rho_x']\approx\\ \frac{a^2}{\rho_0}\rho'_x\)
here the nonlinear terms are neglected and derivatives av \(\rho_0\) set to zero as it's constant.
It is difficult to say how detauled the answer to study question should be, all steps that is neccessary to proof a theory should be possible to follow. Of course we may ask only about specicific parts of each study question which can require shorter answers.
Regards
Ardeshir
Hej,
I was wondering if the given approximation of question 23 should have a minus sign on the RHS instead of the plus sign as in the document.
$$u_j^{n+1} = u_j^n - \frac{a\Delta t}{2\Delta x}\left(u_{j+1}^n - u_{j-1}^n\right)$$
Is that correct?
Thanks in advance!
yes, sorry, this is correct. I updated the questions now.
Philipp
Hej,
I have a question about checking the well-posedness of the backward heat equation presented in the notes of Lecture 4 page 2. If we understood it properly, it says that the backward (implicit) scheme is ill-posed due to amplification of errors. However, performing a Von Neumann analysis, it is the forward (explicit) scheme the one amplificating errors, not the backward. We would like to know if it is a mistake in the lecture notes.
Thank you very much for your attention
Hi,
indeed, the inverse heat equation is ill posed, as the solution will be dominated by amplification of errors. Consider for instance the "natural" occurance of the inverse heat equation, namely the inverse problem of determining the initial distribution of heat if only the state after some time is known. Then the solution (i.e. the distribution at the earlier time) will depend strongly on the known final solution, i.e. the condition that we have a continuous dependence on the initial condition is not satisfied.
This has at that point nothing to do with implicit or explicit discretisation. Of course, one could use the amplification factor from one time to another to see whether you have growing solutions, but the ill-posedness is a property of the PDE rather than the discretisation.
HOpe this helps.
Hej,
I have a few questions about the study questions:
1- You talked above about the absolute stability but I didn't get the point. As for me , if only a region of the plane is stable ,that means that the scheme is not absolutely stable?
2-About question 21), I wrote dow the modified wave equation by using Taylor expansion, but I don't see what type of equation it is? I only know that it would have a dispersive behaviour.
3-About question 25), I don't know how to start, I have begun by trying to find the eigenvalues but I get nowhere.
4-About question 26), I have found the partial differential equations (question d) but I can't find tha analytical solution even if I star from the characteristic formulation.
Thank you very much for your help!
Hi, let my try to give you some hints:
1) yes, this is what absolutely stable means. If a time-integration scheme only has a part of the left-hand side, it might be stable (depending on the time step).
2) The idea is to see what the type of the equation becomes if you only retain the leading order error term (plus of course the terms corresponding to the original PDE). Then you can see what kind of behaviour the error will introduce (dispersion, diffusion).
3) You need to state the conditions for the matrix A if you have a hyperbolic system (what are the eigenvalues and eigenvectors doing).
4) once you have the characteristic form of the equation, you have two independent advection equations, right? So you can construct the solution by combining, in an appropriate way, the solutions of these two advection equations.
Hope this helps, Philipp
Yes, it helps thanks!
I have couple of questions about the study questions:
1- About question 39, how do we combine the stability limits , should we take \(min(\Delta t)\) or should we derive another stability limit using both terms in the equation ? how can it differ for 2D case ?
2- About Euler equations, we tried to turn in into quasi-linear form but we don't know wether should we compute \(\partial F / \partial u\) regarding the conservative variables or \((\rho , u , P)\) ? we tried both of them but non resulted as in the lecture notes. How should we proceed.
regards.
1) There are two ways to combine the stability limits: i) one takes the individual limits from the CFL condition (advection) and the diffusion (viscous limit) and takes the minimum. ii) for the advection -diffusion equation there is a combined limit (see study question 14), that add an additional expression (independent of the spatial grid). However, the derivation is a bit tricky (it has been wrong in the literature for nearly 50 years!). The changes when going to 2D are quite important, and this is what we discussed in the project lecture last week (notes).
2) To get the Euler equations in quasi-linear form, essentially you need to change the variables from the conservative ones (rho, rho u, E) to the primitive ones (rho, u, P). The derivation is a bit tedious, but it work in the end.
Hi,
When looking at question 42, what is the difference between this and Q16? Is there some special form of the advection-diffusion equation that we should use (part a?). And also, it is not stated what spatial discretizaiton to use in 42. I assume FTCS, but then doing "the terms seperately" (part c) gives that advection is unconditionally unstable - one can only get \(\frac{\sigma_{x}^{2}}{\beta_{x}}+\frac{\sigma_{y}^{2}}{\beta_{y}}\le2\) from considering both together. To get normal CFL one needs to use FTBS/FTFS. Or am I missing something?
Thanks
JP
Question 42 is more general about the applicability of the advection/diffusion equation as a model. Therefore, also part c) is more open, and you can choose what scheme to take. Similarly d) does not require you to do the analysis, but rather to explain what you would be doing. When doing it separately, for c) you can also use the CFL condition and assume, that the diffusion is high enough to damp the instability of the central scheme.
Philipp
Ok Thanks, that makes some sense. With regard to part A though, is there some better form of the advection-diffusion equation that would be more suitable? As the regular advection terms do not appear as simply in the NS - or is it just a good trade off between having hyperbolic and elliptic parts and being easy?
One more quick question. When working with the dual grid for the first derivative, we had in lectures that \(\int_{V}\frac{\partial u}{\partial x}dV=\int_{\partial V}udy\). I cannot quite work out why. Applying divergence theory I would get something like \(\int_{V}\frac{\partial u}{\partial x}dV=\int_{\partial V}\left(\begin{array}c u\\0\end{array}\right)\cdot ndS\). I'm sure there is something I am missing but I can't seem to work it out.
Thanks again
Isn't it because \(n_i dS = (dy, -dx)\)?
Right, sorry that makes sense. Thanks!
Hej,
I have a question regarding the second part SQ33, why one does not use an artificial viscosity for upwind schemes.
As we discussed in the lecture, the leading error term of an first order upwind scheme is diffusive, and therefore we wouldn't need an artificial viscosity term, but is this the case for any other order aswell? Or was only a first order upwind scheme assumed in this question?
Thanks in advance,
Randi
Question 37:
Can such a question in this extent really come up in the exam? I mean it is important to understand to concept to derive the Navier-Stokes equations on an arbitrary grid and to see that at the end it is equal to using a CDS on a Cartesian grid, but one needs a long time to do all derivations in part a) and b). And actually it is just a lot of maths...
Q33: yes, it was assumed that the upwind scheme is first order.
Hello
regarding the question 34 can you explain what exactly are the characteristics and the primitive variables?
Dimitris
Hi,
Regarding question 7 : in the c part can we use the same formula as in b to calculate the relative error? And when we use the term absolute error, we mean just the difference between the two values?
Regarding question 24 : can you point out in which lecture pdf can I find the solution?
Thank you in advance
Maria
Maria,
For the question 24 have a look at the lecture notes 10 on the first page.
Mickael
Q34: primitive variables: think of the system as dudt + A*dudx = 0, where u would be velocity and pressure.
conservative variables: think of the system as dvdt + d/dx f(v) = 0, where v might be mass, momentum, energy.
characteristic variables: think of the system as dwdt + B*dwdx = 0 with a diagonal B, such that the components in w are decoupled. This then relates to Riemann invariants, and can be used to determine numerical boundary conditions along characteristics. Note that we have this year NOT discussed that during the lecture.
Philipp
Q7: yes, you can use the same formula. The trick is to realise that you will get a drastic difference between absolute and relative error for the two cases (addition, difference).
Philipp
A more general question regarding consistency:
So we derive an expression for the truncation error and get the accuracy order from the exponents of Delta x respective Delta t. In most examples we had p=q. What happens if p isn't equal to q? Is the scheme then inconsistent? Or is it just the accuracy that is different for time and space discretisation?
Thanks, Randi
p does not need to be the same as q, but it needs to be such that the error really goes down by refining in time or in space. A typical example of a scheme that is NOT consistent is the Dufort Frankel method.
Philipp
So what was the deal with the Q37? I agree with Markus on that!
(Markus Christian Geisenhofer tisdag 17:26)
For Q39, are we taking the 2D case for the Navier Stokes Equations?
Yes.
Q39: I'm not quite sure then how to do the staggered grid because unlike the project, I'm guessing we're dealing with compressible flow. So would we also need to stagger density?
Cheers
We are considering the incompressible flow only.
Question 11 c is regarding the selection of an appropriate time integration scheme for a certain value of %lambda in the Dahlqvist equation. I would like to know the various considerations one would make.
I currently understand the considerations as stability, accuracy and computational memory, but what are their relative order of importance?
for part c) your points are correct. There is no general way of really saying which aspect is most important, it all depends on the specific circumstances you have for the problem at hand, e.g. how difficult is it to invert the matrix for the implicit scheme, how small is the time step really for the explicit one etc. The main answer comes from the consideration of the "time to solution", i.e. how long does the run really take to get a result with a certain accuracy.
for part d) it is important to understand the order of the two schemes, and maybe also look at the "intermediate" scheme, i.e. the Crank-Nicolson scheme. Also, for stiff problems one might need to look at the asymptotic behaviour, e.g. to avoid oscillating solutions.
Hth,
Philipp
Q19: Looking through the lecture notes for determining the Euler equations in conservative form, I understand why the viscous stress is removed, but I'm not quite sure why we also ignore heat dispersion, heat sources and gravity.
The most general form of the compressible Euler equations comprises heat transmission and generation and gravity (and in general body forces).
They are included even in the lecture notes (I am now looking at the first page of lecture8.pdf).
In flow cases where these contributions are absent or negligible, or if you want to simplify the treatment to show certain properties, they can be omitted from the equations, but in general they are present.
May I ask you what lecture notes you are referring to so that I may give a more specific answer?
Kind regards,
Jacopo
Same lecture, a bit further down on the 3rd page. Also searching around on the internet, these terms are generally omitted.
So just to confirm, we would usually be looking at cases where these components are negligible? Would there be any general case when they aren't then or is this a fair assumption?
It always depends on the flow situation which terms need to be taken into account, and which ones can be neglected; see for instance the discussion we had on that in my first lecture (physical modelling etc.). For instance, in aeronautics, gravity (and buoyancy) can usually be neglected, but if you consider problems with natural convection (like the Rayleigh-Bénard problem) these terms are the actual driving force. Similarly, when treating a flow to be inviscid, one would do the same approximation also for the heat diffusion.
Philipp
This is a general question. Do we need to memorise the open forms of the NS equations (continuity, momentum and energy) if, for instance, a question asks for a derivation of the nondimensional NS equations or the boundary layer equations or are they going to be available for us?
Best,
Emirhan
you would need to know the basic governing equations, like the continuity equation, momentum and energy equations, in their respective simplest form (compressible and incompressible). The exam is not about knowing a lot of equations by heart, but rather on testing some of the concepts, which however does require some basic equations.
Philipp
Would it be assume from the expressions for amplification factor for very stiff problems, the implicit scheme works better than crank nicolson?
*safe to
Crank-Nicolson is an implicit scheme as well. What you need to look at is the amplification factor for \(\lambda \Delta t \rightarrow -\infty\) and determine, which of the schemes is closest to the amplification factor of the exact solution during time \(\Delta t\).
Hej! For question 8, we did it in the lesson but we don't really understant why lambda = infinity. Lambda just seemed undefined. For question 16, there is an indication to neglect terms of order 4 but where do those terms come from? Thank you, Ambre
For question 8, you could also switch the denominator and numerator and your slope would then become zero, which is well defined.
In question 16, you get terms of order 4 when considering \xi \delta x = 0 because the approximation of the cosine already contains a square.
In question 16, I cannot get rid of the multiplier \(\xi \Delta x\). I neglect the 4th order term as instructed, but then I get \((\xi\Delta x)^2*f_1(\beta,\sigma) + f_2(\beta)\). Is the final condition supposed to be a function of \(\beta\) and \(\sigma\) only or is it okay to leave the condition in the form I described above?
well, one should get a condition relating sigma and beta, both mulitplied by (\xi \Deltax)^2. Therefore, the latter can be divided by (because it is positive).
Philipp
I realized I was doing some miscalculations, that's why I didn't get a condition of \(f(\sigma, \beta)\). Thanks.
As I read in the previous comments we should know the compressible/incompressible Navier-Stokes, Euler etc. Regarding the formulas for the truncation/ propagation or the varius other equations that we dealt during the lectures should we know these as well or will they be given to us in case they are needed?
Thanks,
Nikos
In case you need truncation errors etc. you would be asked to derive it as part of an exam question. However, you might want to know the Burgers equation, advection equation, diffusion equation etc. and their respective characteristics.
Philipp
Hi!
Question 25. Is a general wave not expressed by u = u_hat*exp(i*(kx-wt)) ? In the study questions the imaginary unit i seems to be missing? According to the lecture notes it sure looks like the i should be there.
Regards
Hello,
if k and omega are complex numbers there is no reason to pre-multiply by i, it is just a matter of how you define k and omega and their real and imaginary parts.
Kind regards,
Jacopo
In questions 29 and 34 the so-called "Characteristic variables" and characteristic formulation are mentioned. What are they? I can't find them in my notes nor on the lecture notes here.
Regards,
Francesco
The characteristic variables are calculated by diagonalising the matrix, so that the new system essentially has the characteristic speed on the diagonal, and can be solved very easily as an ODE. One uses this formulation also to derive proper characteristic boundary conditions, as briefly mentioned in the context of the shock tube. However, we have not discussed this aspect during this year in more detail.
Question 48b:
in the lecture notes it is stated that Vc = h^2. However if we compute Vc with the formula:\(V_c = \frac{1}{2 n_{dim}} \sum_{k=1}^{mc} S_{ck} (x_k - x_c)\)
we will get \(V_c = \frac{1+\sqrt{5}}{3} h^2\). Which is the correct one?
Thanks.
Question 7b and 7c:
I used equation (4) for calculating the relative error for both cases. Regarding the machine accuracy eps_aj, is it correct to use the machine epsilon or do we need to use 1/2 of the machine epsilon?
About the absolute error, is it sufficient to calculate it multiplying the relative error for (x+y) in the first case and (x-y) in the second one or do we need to proceed in another way?
Regards,
Francesco
for b), the epsilon given is directly the relative error.
for c) yes.
Regarding question 48b:
The correct volume is \(h^2\), which you will get if you use the relation
$$V_c = \frac{1}{2 n_{dim}} \sum_{k=1}^{mc} \bar{S}_{ck}\cdot (\bar{x}_k - \bar{x}_c)$$
Note that \(\bar{S}_{ck}\), \(\bar{x}_k\) and \(\bar{x}_c\) are vectors. So you need to account for the the direction of surface normals.
The normal vectors on the faces of dual grid cutting line \(c2\) is \((2/\sqrt{5}, 1/\sqrt{5})\) and on the face cutting line \(c3\) is \((1/\sqrt{5}, 2/\sqrt{5})\).
Philipp Schlatter redigerade 8 januari 2012
Course Responsible
Philipp Schlatter (pschlatt@mech.kth.se) 790 7176, office hours: Fri 14-15Ardeshir Hanifi (hanifi@kth.se) 790 8482, 5550 3197, office hours: Mon 14-15
Course Assistants
Mohammad Hosseini (hosse@mech.kth.se) 790 8034, office hours: Thu 14-17Azad Noorani (azad@mech.kth.se) 790 8034, office hours: Wed 14-17
Literature
Relevant books:
* Numerical Computation of Internal & External Flows, Charles Hirsch, Butterworth-Heinemann, Second Edition, ISBN: 978-0-7506-6594-0.
* Computational Fluid Dynamics, John D. Anderson, Jr., McGraw-Hill, 1995
Lecture notes on Computational Fluid Dynamics (D. Henningson) pdfLecture notes on Basic Numerics (K. Gustavsson) pdfIntroduction to Matlab pdfNotes on FD schemes pdf
Grading
Exam total of 50p,Homework (5 of 6compulsory) 6x2 + project (compulsory) 5 = max 15p.Total points >28 (E), >30 (D), >40 (C), >50 (B), >55 (A).
Philipp Schlatter redigerade 8 januari 2012
Course Responsible
Philipp Schlatter (pschlatt@mech.kth.se) 790 7176, office hours: Fri 14-15Ardeshir Hanifi (hanifi@kth.se) 790 8482, 5550 3197, office hours: Mon 14-15
Course Assistants
Mohammad Hosseini (hosse@mech.kth.se) 790 8034, office hours: Thu 14-17Azad Noorani (azad@mech.kth.se) 790 8034, office hours: Wed 14-17
Literature
Relevant books:
* Numerical Computation of Internal & External Flows, Charles Hirsch, Butterworth-Heinemann, Second Edition, ISBN: 978-0-7506-6594-0.
* Computational Fluid Dynamics, John D. Anderson, Jr., McGraw-Hill, 1995
Lecture notes on Computational Fluid Dynamics (D. Henningson) pdfLecture notes on Basic Numerics (K. Gustavsson) pdfIntroduction to Matlab pdfNotes on FD schemes pdf
Grading
Exam total of 50p,Homework (5 of 6compulsory) 6x2 + project (compulsory) 5 = max 15p.Total points >28 (E), >30 (D), >40 (C), >50 (B), >55 (A).
Course plan to print: pdf
Is there a minimum number of points that one has to achieve in the exam, or is it allowed to score 14 points on the exam if one gets the maximum 15 points from the HW assignments and still pass?
Since PhD students have another project, what will be the number of ECTS coming from this course in case of PhD credits?
Hi Roman,
The points from the HW and from the exam are summed together, and this will give you the grade. The additional requirement is that you hand in 5 (out of 6) homeworks plus you hand in the project. There is no minimum number of points required in the exam to pass.
For PhD students it will be also 7.5 points; the only difference is the course number (either SG2212 or SG3114).
Philipp
Philipp Schlatter redigerade 13 mars 2012
Course Responsible
Philipp Schlatter (pschlatt@mech.kth.se) 790 7176, office hours: Fri 14-15Ardeshir Hanifi (hanifi@kth.se) 790 8482, 5550 3197, office hours: Mon 14-15
Course Assistants
Mohammad Hosseini (hosse@mech.kth.se) 790 8034, office hours: Thu 14-17Azad Noorani (azad@mech.kth.se) 790 8034, office hours: Wed 14-17
Literature
Relevant books:
* Numerical Computation of Internal & External Flows, Charles Hirsch, Butterworth-Heinemann, Second Edition, ISBN: 978-0-7506-6594-0.
* Computational Fluid Dynamics, John D. Anderson, Jr., McGraw-Hill, 1995
Lecture notes on Computational Fluid Dynamics (D. Henningson) pdfLecture notes on Basic Numerics (K. Gustavsson) pdfIntroduction to Matlab pdfNotes on FD schemes pdf
Grading
Exam total of 50p, (closed book exam, i.e. no calculators, books, etc. allowed)Homework (5 of 6compulsory) 6x2 + project (compulsory) 5 = max 15p.Total points >28 (E), >30 (D), >40 (C), >50 (B), >55 (A).
Course plan to print: pdf
Please note that no calculators, books etc. can be used during the exam (closed book exam).
Philipp
Can you give further information on how we should prepare for the exam? What is the main focus?
Will the exam be similiar to the study questions?
Since there is no material allowed to be used for the exam, do we have to be able to derive most of the equations by heart?
Hi,
the questions will be similar to the study questions. The focus is not on learning by heart many equations, but rather on the various concepts (how to do stability, how and where to set boundary conditions, what errors arise, what is the problem of the pressure/projection...). In that sense, we will use simple equations (like the advection equation) and ask about the principles. But the study questions are a good guidance.
Hope this helps,
Philipp
Hi,
I couldn't find any information about the project work that is mandatory for the course.
Please let me know where can I find the info on that.
Koushik
Hi,
The project will be the topic of the course during the last few weeks (see course plan). We have not yet put online the course description yet, but you can consider it similar to a larger homework problem. We will put it online as soon as we have discussed in the course the necessary theory. Is there something specific you would like to know?
Philipp
Okay !
There is nothing specific that I want to know.
Thanks
Koushik
Hej, Do the points awarded for the assignments and project apply for the re-examination as well?
yes, they are valid for the two examinations.
Philipp
Hi,
Can you give us any past exams or any details on the structure of the exam. For example will there be a section for short answers and one for long answers? Are all questions compulsory or can we choose between some?
Thanks,
Amelia
Hi, the exam will be similar to the study questions that are online. All questions together get 50 points, and in that sense mandatory. The questions will be a mix between shorter ones (giving 2-4 points) and longer ones (giving up to 9 points).
Hth,
Philipp
Philipp Schlatter redigerade 8 januari 2012
* Homework 1, due 23/1: fHW1
* Homework 2, due 30/1
* Homework 3, due 6/2
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
Philipp Schlatter redigerade 8 januari 2012
* Homework 1, due 23/1: fHW1
* Homework 2, due 30/1
* Homework 3, due 6/2
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
Philipp Schlatter redigerade 8 januari 2012
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1
* Homework 3, due 6/2
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
Philipp Schlatter redigerade 8 januari 2012
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1
* Homework 3, due 6/2
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
¶
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 8 januari 2012
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1
* Homework 3, due 6/2
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 19 januari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.¶
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1
* Homework 3, due 6/2
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 23 januari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 26 januari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 3 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 3 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 3 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 7 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 7 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4.pdf (Matlab files: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m)
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 7 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4.pdf (Matlab files:
* artificial_visc.m,
* boundary_cond.m, dx.m,
* dx.m
* flux_function.m,
* mac_cormack.m,
* shocktube.m) (main program)
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 10 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4.pdfMatlab files:
* artificial_visc.m
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m
* shocktube.m (main program)
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 10 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdfMatlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m * mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 10 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 16 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 16 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 26 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 26 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_Poisson.m)
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_Poisson.m)
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_Ppoisson.m (updated))
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3 : project.pdf (version 1.05)
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-updated.pdf
* Homework 4, due 13/2: HW4-updated.pdf (see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1
* Homework 2, due 30/1: HW2
* Homework 3, due 6/2: HW3-.pdf (updated.pdf)
* Homework 4, due 13/2: HW4-.pdf (updated.pdf (, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 29 februari 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 1 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 1 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 2 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (100312) pdf (will be updated)
Philipp Schlatter redigerade 2 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (1020312) pdf (will be updated)01) studyquestions_2012.pdf
Ardeshir Hanifi redigerade 2 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (modified) (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 3 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (modified) (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.05)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 3 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (modified) (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.056)Matlab files:
* SG2212_template.m (main program)
* DD_template.m
* avg_template.m
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 7 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (modified) (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.06)Matlab files:
* SG2212_template.m (main program)
* DD_template.mfdaf
* avg_template.m
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 7 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (modified) (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.06)Matlab files:
* SG2212_template.m (main program)
* fdafDD_template.m (updated)
* avg_template.m
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 15 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (modified) (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.06)Matlab files:
* SG2212_template.m (main program)
* DD_template.m (updated)
* avg_template.m
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 15 mars 2012
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 23/1: HW1.pdf
* Homework 2, due 30/1: HW2.pdf
* Homework 3, due 6/2: HW3.pdf (updated)
* Homework 4, due 13/2: HW4.pdf (updated, see comment in Disucssions page)Matlab files:
* artificial_visc.m (updated)
* boundary_cond.m
* dx.m
* flux_function.m
* mac_cormack.m (updated)
* shocktube.m (main program)
* Homework 5, due 27/2: HW5.pdf
* Homework 6, due 5/3: HW6.pdf (modified) (template: help_poisson.m (updated))
* Project, due 19/3: project.pdf (version 1.067)Matlab files:
* SG2212_template.m (main program)
* DD_template.m (updated)
* avg_template.m
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 14 januari 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1:
* Homework 3, due 4/2:
* Homework 4, due 11/2:
* Homework 5, due 25/2:
* Homework 6, due 4/3:
* Project, due 18/3:
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 17 januari 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2:
* Homework 4, due 11/2:
* Homework 5, due 25/2:
* Homework 6, due 4/3:
* Project, due 18/3:
* Study questions (120301) studyquestions_2012.pdf
Hi,
I would recommend to evaluate the exact solution at the same grid points as the numerically integrated one. In the end, for 3b you will get 5 plots, one for each number of discretisation points (N=20, 40...).
Philipp
Philipp Schlatter redigerade 2 februari 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2:
* Homework 6, due 4/3:
* Project, due 18/3:
* Study questions (120301) studyquestions_2012.pdf
I have a question about home work 4 , taks 2 , part b . How should we compute u_l and \rho_l? Should we compute them analytically or we can use the data from the simulation ?
Hi,
The conditions on both sides of the shock should in principle be taken from the solution. That means that for the left side, you take the computed solutions, as stated in the exercise sheet: "...where rho_l and u_l are the computed states at the left-hand side of the shock." On the right side, the flow is not yet processed by the shock, and thus the conditions are unchanged since the beginning of the simulation. The exercise sheet says: "rho_r and u_r are
measured on the right-hand side of the shock and thus given by the initial conditions.".
Hope this helps,
Philipp
Philipp Schlatter redigerade 20 februari 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3:
* Project, due 18/3:
* Study questions (120301) studyquestions_2012.pdf
Philipp Schlatter redigerade 25 februari 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3: HW6.pdf (template: GS_SOR_template.m)
* Project, due 18/3:
* Study questions (120301): studyquestions_2012.pdf
Philipp Schlatter redigerade 25 februari 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3: HW6.pdf (template: GS_SOR_template.m)
* Project, due 18/3: project.pdfMatlab templates: SG2212_template.m, DD_template.m, avg_template.m
* Study questions (120301): studyquestions_2012.pdf
Philipp Schlatter redigerade 27 februari 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3: HW6.pdf (updated!) (template: GS_SOR_template.m, DD_template.m)
* Project, due 18/3: project.pdfMatlab templates: SG2212_template.m, DD_template.m, avg_template.m
* Study questions (120301): studyquestions_2012.pdf
Hi,
a few questions about what was just changed.
It was only the boundary eq on page 2 that was added, right?
The code DD_template, is that accually used at HW6, or is only for the project?
// Jerker
Hi,
I was about to write what we actually changed...
1) the main change is the ordering of the entries in equations (3) and (4), that is which of the coordinates varies the fastest. We have adapted this homework in such a way that it directly can be used in the project to solve the Poisson equation, and we therefore changed the ordering in the code but unfortunately did not adapt the homework sheet. But as it is now, it should be correct (and consistent with the template).
2) DD_template.m can be used for both HW6 and the project; it provides an easy way to compute the 1D derivative matrices which can then made 2D via the kron operator. I guess this will be explained tomorrow.
hope this helps,
Philipp
Philipp Schlatter redigerade 1 mars 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3: HW6.pdf (updated!) (template: GS_SOR_template.m, DD_template.m)
* Project, due 18/3: project.pdf (updated cross references!)Matlab templates: SG2212_template.m, DD_template.m, avg_template.m
* Study questions (120301): studyquestions_2012.pdf
Hi,
I have some difficulties with HW6, to implement the methods in the code.
My problem is that allthough the code converges, it doesn't seem to converge to the solution calculated directly. The valeus are around a factor 2 wrong.
I have search for errors, but can't find any, neither in the direct or iterated function. Have anyone solved this? In that case, should the value P(15Nx+15) (for 30x30) be 0.1083 or 0.0507, or something completely different? So i know where to look for errors...
Hi,
the value in the middle of the domain should be 0.0507...
Best regards,
Philipp
Ok, thank u. Just found that analytically too.. Then the flaw is in the iterative method..
Philipp Schlatter redigerade 4 mars 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3: HW6.pdf (updated!) (template: GS_SOR_template.m, DD_template.m)
* Project, due 18/3: project.pdf (updated cross references!)Matlab templates: SG2212_template.m, DD_template.m, avg_template.m
* Study questions (12303013): studyquestions_20123.pdf
Hi,
We were dealing with the project and we were wondering whether:
1-If we should hand in individual reports although we work together in a group?
2-Will we lose any points if we do not implement the temperature for the Lid-Driven cavity?
Hi,
1) yes, everybody should hand in his own copy, even though it is completely the same. This way we can make sure that each of you has his own copy and comments.
2) no, the temperature is not needed for the credits SG2212.
Philipp
Ardeshir Hanifi redigerade 6 mars 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3: HW6.pdf (updated!) (template: GS_SOR_template.m, DD_template.m)
* Project, due 18/3: project.pdf (updated cross references!)Matlab templates: SG2212_template.m, DD_template.m, avg_template.m
* Study questions (130306): Study questions
Philipp Schlatter redigerade 8 mars 2013
Submit your homeworks (as PDF) using Bilda. However, questions etc. should be asked in KTH Social.
* Homework 1, due 21/1: HW1.pdf
* Homework 2, due 28/1: HW2.pdf
* Homework 3, due 4/2: HW3.pdf
* Homework 4, due 11/2: HW4.pdf Matlab templates: artificial_visc.m, boundary_cond.m, dx.m, flux_function.m, mac_cormack.m, shocktube.m
* Homework 5, due 25/2: HW5.pdf (updated)
* Homework 6, due 4/3: HW6.pdf (updated!) (template: GS_SOR_template.m, DD_template.m)
* Project, due 18/3: project.pdf (updated cross references!)Matlab templates: SG2212_template.m, DD_template.m, avg_template.m
* Study questions (130306): Sstudy questions_2013.pdf (corrected question 23)
What is meant by the question 3.d? what do we mean when we say amplification factor?
I mean amplification factor of the analytical solution,
Hi,
for the analytical solution it has the same meaning that it has for the discretized version, i.e. u^(n+1)/u^n. Do not forget that u^(n+1) = u(t + Delta t) and u^n = u(t).
Regards,
Jacopo
Thank you! also, I wanted to know what do you plot G(z) against? or are we plotting the real part of G(z)?
plot G(z) against z, consider only real values of z
Regards,
Jacopo
Regarding study question 13, i.e. how to derive the stability region for the Crank-Nicolson scheme. Essentially, one gets the amplification factor \(|G|=\frac{|2+Z|}{|2-Z|}\) and the limit for the region of absolute stability is \(|G|=1\). Therefore, one gets the following equality for the border \(|2-Z|=|2+Z|\). The two sides describe a circle with centres at +2 and -2, respectively. The only points where the equality is possible to be fulfilled is the imaginary axis, which then defines the boundary of the region of absolute stability.
Jacopo Canton redigerade 29 januari 2016
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Thursdays at 12:00. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit, please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se).
Please use the following naming convention: "surname_hwX.pdf" and the Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework.¶ Now, the submission using the online system should work for all course participants (including PhD students). Please try, and in case of troubles let us know.
Use only a single pdf and a single archive for your homeworks. Preferably scan your homework, if you take a photo, make sure it is sharp and bright. ¶
HOMEWORK GUIDELINES:¶
* Five assignements out of six are mandatory;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
¶
¶
HOMEWORKS:
* Homework 1, due 28/1: HW1.pdf (update of task 3c)
* Homework 2, due 4/2: HW2.pdf
* Homework 3, due 11/2:
* Homework 4, due 18/2: Matlab templates:
* Homework 5, due 25/2:
* Homework 6, due 2/3: Matlab templates:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Erik Boström redigerade 3 februari 2016
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Thursdays at 12:00. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit, please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se).
Now, the submission using the online system should work for all course participants (including PhD students). Please try, and in case of troubles let us know.
HOMEWORK GUIDELINES:
* Five assignements out of six are mandatory;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 28/1: HW1.pdf (update of task 3c)
* Homework 2, due 4/2: HW2.pdf
* Homework 3, due 11/2: HW3.pdf
* Homework 4, due 18/2: Matlab templates:
* Homework 5, due 25/2:
* Homework 6, due 2/3: Matlab templates:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Jacopo Canton redigerade 12 februari 2016
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Thursdays at 12:00. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit, please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se).
Now, the submission using the online system should work for all course participants (including PhD students). Please try, and in case of troubles let us know.
HOMEWORK GUIDELINES:
* Five assignements out of six are mandatory;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 28/1: HW1.pdf (update of task 3c)
* Homework 2, due 4/2: HW2.pdf
* Homework 3, due 11/2: HW3.pdf
* Homework 4, due 18/2: Matlab templates: HW4.pdf
* Homework 5, due 25/2:
* Homework 6, due 2/3: Matlab templates:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Erik Boström redigerade 19 februari 2016
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Thursdays at 12:00. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit, please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se).
Now, the submission using the online system should work for all course participants (including PhD students). Please try, and in case of troubles let us know.
HOMEWORK GUIDELINES:
* Five assignements out of six are mandatory;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 28/1: HW1.pdf (update of task 3c)
* Homework 2, due 4/2: HW2.pdf
* Homework 3, due 11/2: HW3.pdf
* Homework 4, due 18/2: HW4.pdf
* Homework 5, due 25/2: HW5.pdf, HW5_m-files.zip
* Homework 6, due 2/3: Matlab templates:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Jacopo Canton redigerade 21 februari 2016
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Thursdays at 12:00. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit, please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se).
Now, the submission using the online system should work for all course participants (including PhD students). Please try, and in case of troubles let us know.
HOMEWORK GUIDELINES:
* Five assignements out of six are mandatory;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 28/1: HW1.pdf (update of task 3c)
* Homework 2, due 4/2: HW2.pdf
* Homework 3, due 11/2: HW3.pdf
* Homework 4, due 18/2: HW4.pdf
* Homework 5, due 25/2: HW5_updated.pdf, HW5_m-files.zip
* Homework 6, due 2/3: Matlab templates:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
There was a mistake in equation (2) of Homework 5, now the pdf is correct.
Jacopo Canton redigerade 27 februari 2016
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Thursdays at 12:00. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit, please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se).
Now, the submission using the online system should work for all course participants (including PhD students). Please try, and in case of troubles let us know.
HOMEWORK GUIDELINES:
* Five assignements out of six are mandatory;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 28/1: HW1.pdf (update of task 3c)
* Homework 2, due 4/2: HW2.pdf
* Homework 3, due 11/2: HW3.pdf
* Homework 4, due 18/2: HW4.pdf
* Homework 5, due 25/2: HW5_updated.pdf, HW5_m-files.zip
* Homework 6, due 21/3: Matlab templates: at midnight: HW6.pdf HW6_mFiles.zip
* Project, due 23/3: project.pdfMatlab templates: project_mFiles.zip
* Study questions: studyquestions_2015.pdf
Jacopo Canton redigerade 18 januari 2017
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Tuesdays at 23:59. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit (mostly PhD students in the beginning of the course), please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se).
HOMEWORK GUIDELINES:
* Five homeworks out of six are mandatory;
* approx. 75% correct is required in each homework to pass;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* You can work in groups up to 3;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 24/1: HW1.pdf
* Homework 2, due 31/1:
* Homework 3, due 7/2:
* Homework 4, due 14/2:
* Homework 5, due 21/2:
* Homework 6, due 28/2:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Erik Boström redigerade 25 januari 2017
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Tuesdays at 23:59. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit (everybody should be added to the online system by now!), please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se). But only if the other option does not work!
HOMEWORK GUIDELINES:
* Five homeworks out of six are mandatory;
* approx. 75% correct is required in each homework to pass;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* You can work in groups up to 3;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 24/1: HW1.pdf
* Homework 2, due 31/1: HW2.pdf
* Homework 3, due 7/2:
* Homework 4, due 14/2:
* Homework 5, due 21/2:
* Homework 6, due 28/2:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Jacopo Canton redigerade 27 januari 2017
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Tuesdays at 23:59. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit (everybody should be added to the online system by now!), please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se). But only if the other option does not work!
HOMEWORK GUIDELINES:
* Five homeworks out of six are mandatory;
* approx. 75% correct is required in each homework to pass;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* You can work in groups up to 3;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
HOMEWORKS:
* Homework 1, due 24/1: HW1.pdf
* Homework 2, due 31/1: HW2_updated.pdf
* Homework 3, due 7/2:
* Homework 4, due 14/2:
* Homework 5, due 21/2:
* Homework 6, due 28/2:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Jacopo Canton redigerade 30 januari 2017
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Tuesdays at 23:59. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit (everybody should be added to the online system by now!), please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se). But only if the other option does not work!
HOMEWORK GUIDELINES:
* Five homeworks out of six are mandatory;
* approx. 75% correct is required in each homework to pass;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* You can work in groups up to 3;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single archive: "surname_hwX.zip". X is the number of the homework;
If you fail a homework take a look at the corrected versions that we upload: you will find comments about your work and instructions about what to do to repair.The deadline for uploading your corrections is the day of the exam.¶
HOMEWORKS:
* Homework 1, due 24/1: HW1.pdf
* Homework 2, due 31/1: HW2_updated.pdf
* Homework 3, due 7/2:
* Homework 4, due 14/2:
* Homework 5, due 21/2:
* Homework 6, due 28/2:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Jacopo Canton redigerade 2 februari 2017
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Tuesdays at 23:59. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit (everybody should be added to the online system by now!), please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se). But only if the other option does not work!
HOMEWORK GUIDELINES:
* Five homeworks out of six are mandatory;
* approx. 75% correct is required in each homework to pass;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* You can work in groups up to 3;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single separate archive: "surname_hwX.zip". X is the number of the homework;
If you fail a homework take a look at the corrected versions that we upload: you will find comments about your work and instructions about what to do to repair.The deadline for uploading your corrections is the day of the exam.
HOMEWORKS:
* Homework 1, due 24/1: HW1.pdf
* Homework 2, due 31/1: HW2_updated.pdf
* Homework 3, due 7/2: HW3.pdf
* Homework 4, due 14/2:
* Homework 5, due 21/2:
* Homework 6, due 28/2:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Jacopo Canton redigerade 14 februari 2017
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Tuesdays at 23:59. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit (everybody should be added to the online system by now!), please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se). But only if the other option does not work!
HOMEWORK GUIDELINES:
* Five homeworks out of six are mandatory;
* approx. 75% correct is required in each homework to pass;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* You can work in groups up to 3;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single separate archive: "surname_hwX.zip". X is the number of the homework;
If you fail a homework take a look at the corrected versions that we upload: you will find comments about your work and instructions about what to do to repair.The deadline for uploading your corrections is the day of the exam.
HOMEWORKS:
* Homework 1, due 24/1: HW1.pdf
* Homework 2, due 31/1: HW2_updated.pdf
* Homework 3, due 7/2: HW3.pdf
* Homework 4, due 14/2: HW4.pdf, HW4_m-files.zip
* Homework 5, due 21/2: HW5.pdf
* Homework 6, due 28/2:
* Project, due 23/3: Matlab templates:
* Study questions: studyquestions_2015.pdf
Erik Boström redigerade 22 februari 2017
Submit your homework (as PDF) using KTH Social using the link "Assignments" on the left menu at the latest on Tuesdays at 23:59. Questions etc. should be asked in KTH Social on this page. In case of problems or that you do not have the link to submit (everybody should be added to the online system by now!), please hand in the homework via email (erikbos@mech.kth.se or jcanton@mech.kth.se). But only if the other option does not work!
HOMEWORK GUIDELINES:
* Five homeworks out of six are mandatory;
* approx. 75% correct is required in each homework to pass;
* Respect the deadline;
* Use only a single pdf. Preferably scan your homework, if you take a photo, make sure it is sharp and bright;
* Include all plots in the pdf in the right place;
* Do not present plots without commenting them: always write a (short) description of what the plot tells you and what you can conclude from it;
* You can work in groups up to 3;
* If you work in groups:
* write the names of all group members at the beginning of the report;
* you can work and discuss together but each group member is required to submit an individual report written with his/her own words; copy-paste reports will not be accepted (see cheating and plagiarism);
* Please use the following naming convention: "surname_hwX.pdf" and include all Matlab files as a single separate archive: "surname_hwX.zip". X is the number of the homework;
If you fail a homework take a look at the corrected versions that we upload: you will find comments about your work and instructions about what to do to repair.The deadline for uploading your corrections is the day of the exam.
HOMEWORKS:
* Homework 1, due 24/1: HW1.pdf
* Homework 2, due 31/1: HW2_updated.pdf
* Homework 3, due 7/2: HW3.pdf
* Homework 4, due 14/2: HW4.pdf, HW4_m-files.zip
* Homework 5, due 21/2: HW5.pdf
* Homework 6, due 28/2: HW6.pdf, HW6_m-files.zip
* Project, due 23/3: Matlab templates: project.pdf, project_m-files.zip
* Study questions: studyquestions_2015.pdf
Lärare Philipp Schlatter redigerade 13 maj 2013
[Titel saknas]Omtenta
Philipp Schlatter redigerade 8 januari 2012
TentameRe-Examination
Lärare Philipp Schlatter redigerade 13 mars 2012
closed book exam, i.e. no books, calculators etc. allowed.¶
Schemahandläggare ställde in händelsen 23 mars 2012
Schemahandläggare redigerade 31 mars 2012
[u'SG2212V1']
Philipp Schlatter redigerade 23 januari 2012
Here are some interesting links to numerical simulations:
List of supercomputers: www.top500.org (current list)
Flow gallery of the Swedish e-Science Research Centre (SeRC):http://www.e-science.se/information/flow-gallery
Linné FLOW Centre
Hej,
I have a mathematical question concerning study question 21:
How is the mathematical way to follow from the advection equation u_t=-a*u_x that u_tt=a^2*u_xx?
Thank you!