# FSG3114 Numerical Methods in Fluid Mechanics 7.5 credits

#### Numeriska metoder i strömningsmekanik

An in-depth course on numerical methods for computer simulation of fluid flows. Together with SG2213 Applied Computational Fluid Dynamics, a comprehensive course on theory and practice of computational fluid dynamics.

### Offering and execution

#### No offering selected

Select the semester and course offering above to get information from the correct course syllabus and course offering.

## Course information

### Content and learning outcomes

#### Course contents *

Short introduction with review of other numerical methods or the basic equations of fluid dynamics (the class will be divided in two groups). Conservation laws: the Navier-Stokes equations. Different levels of approximation, the Euler and Reynolds Averaged equations. Turbulence models. Basics of finite approximations for partial differential equations. Mathematical properties of hyperbolic systems. Numerical treatment of shocks. Finite volume and finite element methods. Boundary conditions. High-resolution methods. Grid generation. Practical algorithms for compressible and incompressible flow. Computer exercises with methods for the Euler equations in 1D and different approximations for 2D compressible and incompressible flows.

#### Intended learning outcomes *

After reading this course the student should be:

• familiar with the differential equations for flow phenomena and numerical methods for their solution
• able to use and develop flow simulation software for the most important classes of flows in engineering and science.
• able to critically analyse different mathematical models and computational methods for flow simulations
• able undertake flow computations using current best practice for model and method selection, and assessment of the quality of results obtained.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

A course in computer science or programming (e.g. DD1331).
Background in either fluid dynamics or numerical methods, corresponding to one of the second level courses in numerical methods (e.g. SF2520) or a course in fluid dynamics (e.g. SG2214) or equivalent.

#### Recommended prerequisites

• A course in computer science or programming (e.g. DD1342);
• Background in either fluid dynamics or numerical methods, corresponding to one of the second level courses in numerical methods DN2220-DN2225, DN2250-DN2260, DN2266, or a course in fluid dymamics e.g. SG2214 or equivalent.

#### Equipment

No information inserted

#### Literature

To be announced at course start. In 08/09: Numerical Computation of Internal & External Flows, Charles Hirsh, Butterworth-Heineman, Second Edition, ISBN: 978-0-7506-6594-0, was used.

### Examination and completion

P, F

#### Examination *

• LAB1 - Computer exercise, 3.0 credits, Grading scale: P, F
• PRO1 - Project work, 1.5 credits, Grading scale: P, F
• TEN1 - Exam, 3.0 credits, Grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

#### Other requirements for final grade *

One written examination with minimum performance that corresponds to grade B for the Master's course SG2212 (TEN1), 3.0 h.p.
Homework and computer assignments (LAB1), 3.0 h.p. Project work (PRO1), 1.5 h.p.

#### Opportunity to complete the requirements via supplementary examination

No information inserted

#### Opportunity to raise an approved grade via renewed examination

No information inserted

### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web FSG3114

SCI/Mechanics

#### Main field of study *

No information inserted

#### Education cycle *

Third cycle

SG2213 Applied Computational Fluid Dynamics covers selected industrial and research topics in students projects with invited specialists.

#### Contact

Philipp Schlatter

#### Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.