Abstract
We are concerned with theoretical modelling of unsteady, twodimensional detonation waves in high energy solids. A mathematical model and a numerical method to solve the associated hyperbolic system of equations are presented. The model consists of the Euler equations augmented by extra conservation laws and source terms to account for chemical reaction and tracking of materials. Both the thermodynamics and the chemistry are treated in a simple way. Using a detonation analogue due to Fickett, we test several numerical methods and assess their performance in modelling the essential features of detonation waves. The numerical method selected for the full model is an extension of the conservative, shock capturing technique of Roe, together with an adaptive mesh refinement procedure that allows the resolution of fine features such as reaction zones. Results for some typical tests problems are presented.
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