Modelling detonation waves in heterogeneous energetic materials

Abstract

The computation of detonation waves in heterogeneous explosives involves compressible multiphase mixtures due to the chemical decomposition of the energetic material as well as its heterogeneous initial formulation. Also material interfaces are present between the explosive and the surrounding inert or reactive materials. We develop a new method for the modelling of interface problems and multiphase mixtures in the particular limit where phases pressures and velocities relax towards equilibrium very fast. This method is a variant of the discrete equations for multiphase mixtures proposed by Abgrall and Saurel [J. Comput. Phys. 186 (2) (2003) 361]. The new discrete model is adapted to reacting flows with mass, momentum and energy transfer. The model is based on the pure material equation of state only (no mixture equation of state is used) for the computation of the reaction zone of detonation waves. The algorithm is full Eulerian and fulfills interface conditions between mixtures and pure materials automatically. It is validated over a set of difficult test problems with exact solution and its multi-dimensional capabilities are shown over problems involving a large number of materials.