Thomas Harbreteau

Trying to solve analytically PDE’s systems from physics is in most cases a doomed enterprise. This is where scientific calculus comes into play. This domain of mathematics concerns the study and development of algorithms, called numerical schemes, to compute approximate solutions to PDE’s, even when the existence of such a solution is still an open problem (hello Navier-Stokes equations).

 

Hyperbolic conservation laws are a type of PDE’s that play a major role

in fluid dynamics. In this talk, we will focus on a historical, and still widely used method to solve these equations : Godunov’s method. It is based on finite volumes schemes, where the intercell fluxes are computed thanks to exact or approximate Riemann solvers.

 

The goal of this presentation is not to do a detailed analysis of these methods, but to present general concepts and problematics of computational fluid dynamics through the example of the 1D Burger’s equation, the simplest equation that highlights the specificity of hyperbolic conservation laws.