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)

 

Recommended prerequisite

M1 MMS mandatory courses

 

 

Number of hours

  • CM : 27
  • TD : 12

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

Number of hours 39

Level of study Master degree level

Contact(s)

Organizational unit

Administrative contact(s)

Secrétariat de Mathématiques - Brigitte GAUBERT

Email : brigitte.gaubert @ univ-pau.fr

Places

  • Pau