A scheme for detonation wave computation on moving meshes

A method for computing detonation waves on moving meshes is described. The detonation process is simulated by solving two-dimensional gas dynamics equations and a chemical reaction equation written in integral form. The numerical method is based on a Godunov-type scheme of second-order accuracy in time and space. The burning zone is resolved by applying adaptive mesh refinement. At every instant of time, the mesh is constructed by minimizing a Dirichlet functional. Numerical results are presented for the one-dimensional Chapman–Jouguet detonation and for unstable overdriven detonation in one and two space dimensions.