Abstract: We consider the Riemann problem for the two-phase model, proposed by Baer and Nunziato in [{\it Int.\ J.\ of Multiphase Flows}, {\bf 12}, 861-889 (1986)]. It describes the flame spread and the deflagration-to-detonation transition (DDT) in gas-permeable, reactive granular materials. The model is given by the non-strictly hyperbolic, non-conservative system of partial differential equations. We investigate the structure of the Riemann problem and construct the exact solution for it. Furthermore, we define a weak solution for it and propose a number of test cases. Under certain conditions, the two-phase flow equations reduce to the Euler equations in the duct of variable cross section. Consequently, our construction of the exact solution applies also to this system.
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