DN2275 Advanced Computation in Fluid Mechanics 7.5 credits

Avancerade beräkningsmetoder i flödesmekanik

An advanced trans-disciplinary course approaching fundamental problems in fluid mechanics of major practical importance by advanced tools from mathematical analysis and numerical analysis, using modern computational technology.

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

Navier-Stokes equations, Eulers equations, existence of exact solution, weak solution , weak uniqueness, General GAlerkin (G2) method, energy estimates, perturbation growth, stability, duality, a posteriori error estimate and adaptivity.

Friction boundary condition, separation, boundary layer, generation of drag and lift, Magnus effect, d’Alembert’s paradox.

Intended learning outcomes *

The goal is that the students should be able to analyze and use General GAlerkin (G2) adaptive finite element computational technology to model fluid flow at hogh Reynolds numbers. More precisely this means that the students should be able to:

  • define the concepts weak solution and weak uniqueness
  • derive energy estimates for the underlying equations and G2 approximations
  • derive a posteriori output error estimates for G2 using duality
  • analyze the gloal effect of friction boundary conditions in G2 computations
  • use G2 software for adaptive flow computations with error control.

Based on a critical review of research literature and the students own G2 computations, the student should be able to compare state of the art fluid mechanics with G2 computation/analysis concerning the following fundamental problems:

 turbulence

 separation

 generation of drag and lift

with applications in a number of areas such as car-, ship- and aircraft industry and ball sports. The purpose is to develop a critical approach with the possibility to question established truths, and form new hypotheses.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

Single course students: 90 university credits including 45 university credits in Mathematics or Information Technology. English B, or equivalent.

Recommended prerequisites

The course DN2260/SF2561 Finite element methods.

Equipment

No information inserted

Literature

J. Hoffman and C. Johnson (2007) "Computational Turbulent Incompressible Flow", and a number of scientific papers (to be handed out at course start).

Examination and completion

Grading scale *

A, B, C, D, E, FX, F

Examination *

  • PRO1 - Project, 4.0 credits, Grading scale: P, F
  • TEN1 - Examination, 3.5 credits, Grading scale: A, B, C, D, E, FX, 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.

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

Other requirements for final grade *

Mandatory participation at seminars including preparing short summary of preparatory literature. Assignements (4 hp). Project (3.5 hp).

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Johan Hoffman

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 DN2275

Offered by

SCI/Mathematics

Main field of study *

No information inserted

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

Johan Hoffman, tel: 790 7783, e-post: jhoffman@kth.se

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.