Number of hours
- Lectures 9.0
- Tutorials 9.0
ECTS
ECTS 1.75
Goal(s)
The aim of this course is to provide an overview of finite volume methods for the numerical solution of conservation laws, as well as methods for the solution of coupled problems (multiscale and/or multiphysics phenomena, as encountered for example in fluid mechanics).
Contact Eric BLAYO
Content(s)
Part 1: "Coupling"
Introduction : interactions of different scales, coupled phenomena
Coupling methods : Schwarz methods, optimized interface conditions, Mortar elements
Introduction to multigrid methods
Part 2: finite volume methods
- Generalities on properties of numerical schemes (stability, accuracy...)
- Derivation of efficient numerical schemes (finite volume schemes) for hyperbolic equations, with illustration on 3 examples (advection equation, equation simulating car traffic, shallow water equation for simulating a dam break)
Prerequisites
Numerical methods for PDEs (finite differences, finite elements), basic linear algebra
Test
Written exam
N1=0.5*TP+0.5*E1
N2=0.5*TP+0.5*E2
Bibliography
Trottenberg U., C.W. Oosterlee and A. Schuller, 2000 : Multigrid. Academic Press
Valli A. and A. Quarteroni, 1999 : Domain decomposition methods for PDEs Oxford University Press