Course Syllabus for

Numerical Simulations of Flow Problems
Numeriska simuleringar av flödesproblem

FMNN40F, 7.5 credits

Valid from: Spring 2023
Decided by: Maria Sandsten
Date of establishment: 2022-12-22

General Information

Division: Numerical Analysis
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course codes: NUMN28, FMNN40
Teaching language: English


The overall goal of the course is that the graduate student should acquire basic knowledge in modern numerical methods for non-linear conservation laws, with a focus on fluid models. Important examples of such models are the Euler equations of gas dynamicsand the shallow water equations, both of which are simplifications of the Navier-Stokes equations. These models are used in the design of aircraft and wind turbines, as well as in climate system research. The course discusses so called finite volume methods for discretizing the models -- their derivation, convergence and stability properties, --- and touches upon higher order extensions. The discretization often leads to large nonlinear systems of equations. The course presents iterative methods for solving these -- such as Multigrid and Newton-Krylov. Their convergence properties are discussed, with a particular focus on systems arising from the above discretizations.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Judgement and Approach

For a passing grade the doctoral student must

Course Contents

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

Course Literature

First title also as Ebook.

Instruction Details

Types of instruction: Lectures, project, miscellaneous. Apart from lectures and a compulsory (final) project there are assignments. These are not compulsory but provides useful preparations for the project.

Examination Details

Examination formats: Oral exam, written report. The examination consists of a written report of the 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.
Grading scale: Failed, pass

Admission Details

Admission requirements: FMNN10 Numerical Methods for Differential Equations
Assumed prior knowledge: FMAN35 Calculus in Several Variables and FMAN55 Applied Mathematics.

Course Occasion Information

Contact and Other Information

Course coordinators:
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