Dependence Of Qualitative Behavior Of The Numerical Solutions On The Ignition Temperature For A Combustion Model
Xin-ting Zhang 1, Lung-an Ying 11 Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
We study the dependence of qualitative behavior of the numerical solutions (obtained by a projective and upwind finite difference scheme) on the ignition temperature for a combustion model problem with general initial condition. Convergence to weak solution is proved under the Courant-Friedrichs-Lewy condition. Some condition on the ignition temperature is given to guarantee the solution containing a strong detonation wave or a weak detonation wave. Finally, we give some numerical examples which show that a strong detonation wave can be transformed to a weak detonation wave under some well-chosen ignition temperature.
Key words: Detonation wave solutions; Combustion model; Upwind finite difference scheme.