### 2003-07

#### The Riemann problem for the Baer-Nunziato model of two-phase flows

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