REACTION-DIFFUSION EQUATIONS IN COMBUSTION

1.Scott-Wang-Showalter model of reaction and difussion 2.Numerical methods 3.Numerical results 4.ConclusionTarget patterns have been observed experimentally during combustion of premixed gases. To interpret these observations, we exploit a simple model, the Salnikov scheme involving two reaction steps with an Arrhenius temperature dependence. The mass and energy balance equations governing the temporal evolution of the intermediate species concentration and the reacting mixture temperature lead up to the reaction-diffusion system consisting of two partial differential equations whose dimensionless variant is the Scott-Wang-Showalter model. We used finite difference method and finite volume methods for the spatial discretization of the system. We approach the finite volume methods in cases where an advection term is included in the system. A time discretization is arranged by the semi-implicit time-stepping scheme. Target patterns and an influence of the advection were simulated. We will present numerical results of the several cases