NUMN28 Numerical Simulations of Flow Problems, 7.5 credits, is an elective course for a Master of Science degree in mathematics. The course can be taken as a stand-alone course. The course is given at half-study pace during the second half of each spring semester. The course is given in English.

Course Content
The course covers

Models of computational fluid dynamics
Hyperbolic conservation laws and their basic properties (weak solutions, weak entropy solutions, shocks)
Discontinuous Galerkin discretizations
Simulations of gas dynamics
Krylov subspace methods with preconditioning
Jacobian-free Newton-Krylov methods
Multigrid methods for flow problems

Teaching
The teaching consists of lectures. Assignments and a compulsory final project are included in the course. The assignments are not compulsory, but they are preparatory for the compulsory final project.

Assessment
The examination consists of a written report of the final project and an appurtenant oral examination based on the report. The oral examination is only given to those students who have passed the written report.

Course Literature

Randall J. LeVeque, Numerical Methods for Conservation Laws, 1992, ISBN 764327235.
Philipp Birken, Numerical Methods for the Unsteady Navier-Stokes Equations, 2012, pdf.Links to an external site.
Philipp Birken, Numerical Methods for Unsteady Compressible Flow Problems, CRC Press, 2021.

Official Course Description

Syllabus in English
Kursplan på svenska

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Numerical Analysis at Faculty of Science