 # Finite Volume Methods for Hyperbolic Systems / Asmptotic Methods

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## Finite Volume Methods for Hyperbolic Systems / Asmptotic Methods

### Objectives

In alternate years:

Finite volume schemes for hyperbolic systems and compressible fluid mechanics

This lesson deals with theorical and numerical analysis of finite volume schemes for linear and non linear hyperbolic systems

Asymptotic Methods: training about usual techniques for problems with small parameters (BKW method, asymptotic expansions, thin-layer models)

#### Number of hours

• Travaux Dirigés : 12h
• Cours Magistral : 27h

### Form of assessment

 First session Second session Continuous assessment: 50% Final examination: 50% Final examination length: 2 hours Remedial examination: 100 % Remedial examination length: 2 hours

### Syllabus

In alternate years:

Finite volume schemes for hyperbolic systems and compressible fluid mechanics:

1- Presentation of the compressible Navier-Stokes equations.

Adimensioning. Caracteristic numbers : Prandtl, Reynolds, Mach.

Presentation of different systems induced by the compressible Navier-Stokes equations : low Mach model, Euler system. Some classicals flows.

2- Burgers equation. Traffic flow model. Caracteristic method. Choc, weak and entropic solution. Riemann problem for hyperbolic equations.

3- Finite volume schemes for hyperbolic equations. Kruzhkov and Hou LeFloch theorem, Godunov scheme. Linearized numerical flux (ex : Lax-Friedrich).

4- Hyperbolic systems : definitions and simple examples.

5- Euler system, flows with pistons on the left and right. Contact surface.

Full resolution of the Riemann problem.

6- Linearized numerical fluxes for Euler equations.

Asymptotic Methods:

In this course, we deal with elliptic problem with small parameters. The program is divided in 3 tracks:

1- BKW methods for boundary layers

2- Small-obstacles problems

3- Thin-layers problems

### In brief

ECTS credits 4.0

Number of hours 39.0

Level of study Master degree level