A Finite Volume Scheme for a Nonlinear Reaction-Diffusion PDE Arising in Combustion
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.
KeywordsControl Volume Finite Volume Implicit Scheme Nonlinear Parabolic Equation Robin Boundary Condition
Unable to display preview. Download preview PDF.
- 1.R. Eymard, T. Gallouët, and R. Herbin, Handbook of Numerical Analysis, Vol. VII, North Holland, 2000.Google Scholar