A simple model permitting the numerical simulation of shocks, detonations, and shock-to-detonation transition

A method for simulating the propagation of discontinuities (shocks or detonations) is presented. Consideration is given to the modification of the hydrodynamic treatment due to the presence of a discontinuity, to the evolution of the discontinuities, and to the treatment of boundaries. The numerical simulation method takes into account the jumps of thermodynamic quantities, gives better results than traditional methods which affect discontinuities with numerical viscosity and chemical reactions, and can even be used for relatively coarse meshes. A supplementary hypothesis which permits the continuous treatment of the shock-to-detonation transition is also examined.