Abstract: 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 deformed 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 solution singularity, which allows placing several cells into the burning zone and, thus, resolving a fine structure of the reaction front. The numerical examples relating to the Chapman-Jouguet detonation and unstable overdriven detonation are considered in both one and two space dimensions.
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