Numerical Methods And Their Relating Problems For A Combustion Model

This dissertation is concerned with the numerical methods for the simplest CJ model and the uniform formula for its Riemann solutions.We set up a finite difference method to simulate strong detonation waves and Chapman-Jouguet detonation waves. Under a stability condition the norm estimates are given. Then con-vergence for the Riemann problem is proved. Some numerical experiments are presented.We set up another finite difference method to simulate Chapman-Jouguet deflagration waves. Under a stability condition the norm estimates are given. Then convergence for the Riemann problem is also proved. Some numerical experiments are presented.We have also considered the more general initial data. We set up a uniform algorithm so that all kinds of combustion waves in simplest CJ model can be simulated, including strong detonation waves, Chapman-Jouguet detonation waves, Chapman-Jouguet deflagration waves and contact discontinuities.At last, we construct a uniform formula for the Riemann solutions. We define a functional, then the Riemann solutions can be given by the maximum value point of this functional.