Approches numériques par des volumes finis d’une équation de transport

Abstract

The purpose of this thesis is to study numerically by two methods, the method of .finite Differences and finite volume method that applies to the advection-diffusion equation, Represented as a transportation problem in R. A simple modeling of the propagation of a cloud of smoke, we show the existence and Uniqueness of the solution without diffusion using the method of characteristics. The finite difference method is first applied to the problem. Then he was treated with the finite volume method and we give a proof of the stability and convergence. The study by two numerical methods are illustrated by numerical tests on cases eli- gible Mesh.