A Finite Volume Scheme for a Nonlinear Reaction-Diffusion PDE Arising in Combustion

Abstract

The aim of this paper is to describe a finite volume scheme for the numerical discretization of a reaction-diffusion equation arising in the modelling of titanium carbide exothermic combustion synthesis. The paper is organized as follows. In section two, the mathematical modelling is formulated. Section three outlines the finite volume discretization principles. In section four, an L _∞ stability result of the numerical scheme for both the nonlinear parabolic equation and the kinetics equation is established. Section five analyses the stability of the implicit scheme. The last section presents some numerical results.