Numerical study on the reactive euler equation based on semi-implicit methods

This paper introduces an IMEX (implicit-explicit) Additive Runge-Kutta method, which was applied to resolve the stiff source term into the stiff part and non-stiff part, and the stiff part was solved implicitly while the non-stiff part was handled explicitly. The numerical calculation of the gas-phase detonation show that the method can deal with the stiff problems caused by the source term, accurate capture the discontinuity and description of the structure of the Mach reflection, meanwhile the features of cellular pattern agree well with the experimental results.