Second-order Godunov-type scheme for reactive flow calculations on moving meshes

The method of calculating the system of gas dynamics equations coupled with the chemical reaction equation is considered. The flow parameters are updated in whole without splitting the system into a hydrodynamical part and an ODE part. The numerical algorithm is based on the Godunov’s scheme on deforming meshes with some modification to increase the scheme-order in time and space. The variational approach is applied to generate the moving adaptive mesh. At every time step the functional of smoothness, written on the graph of the control function, is minimized. The grid-lines are condensed in the vicinity of the main solution singularities, e.g., precursor shock, fire zones, intensive transverse shocks, and slip lines, which allows resolving a fine structure of the reaction domain. The numerical examples relating to the Chapman–Jouguet detonation and unstable overdriven detonation are considered in both one and two space dimensions.