About The Theoretical And Numerical Analysis Of Combustion Problems

In this paper we mainly study one dimensional combustion problem both theoretically and numerically. In theory we review three important combustion models: Majda's model, C-J model and Z-N-D model. Where, C-J model and Z-N-D model can be deriveded by Majda's model under C-J theory and Z-N-D theory seperately. We solve the Riemann problem for C-J model and Z-N-D model under the entropy conditions. Numerically on one hand we approximate the combustion solutions by using the following three schemes: the scheme which is the first order both in time and space(Godunov scheme), the scheme which is the second order in time and is the first order in space, and the scheme which is the second order both in time and space(GRP scheme). On the other hand we approximate the linear equation, the nonlinear equation and the combustion equation by using GRP scheme. Then we study the solutions under different CFL conditions. Finally we analyze the results of the linear equation by using the modified equation associated with GRP scheme.