by Andrianov, N., Warnecke, G..

**Series:** 2003-07, Preprints

- MSC:
- 35L65 Conservation laws
- 35L67 Shocks and singularities

**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.

**Keywords:**

Two-phase flow, non-conservative hyperbolic equations, evolutionarity