The Riemann problem for the Baer-Nuziato two-phase flow model

We consider the Riemann problem for the two-phase flow model, proposed by Baer and Nunziato, [Int. J. Multiphase Flows 12 (1986) 861]. It describes the flame spread and the deflagration-to-detonation transition (DDT) in gas-permeable, reactive granular materials. The model is given by a 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. We establish that the solution across one wave is not unique and propose to use the evolutionarity criterion to single out the admissible solution. Due to special structure of the Riemann problem for the Baer-Nunziato model, we are able to introduce a notion of a weak solution for it. Finally, we propose a number of test cases, based on the exact solution to the Riemann problem for the Baer-Nunziato model.