An exact Riemann solver for compressible two-phase flow models containing non-conservative products

In this article we present a new numerical procedure for solving exactly the Riemann problem of compressible two-phase flow models containing non-conservative products. These products appear in the expressions for the interactions between the two phases. Thus, in the compressible limit, the governing equations are hyperbolic but can not be written as conservation laws, i.e. in divergence form. In general, the solution to the Riemann problem of these models contains six distinct centered waves. According to the relative position of these waves in the x–t plane, the possible solutions can be classified into four principal configurations. The Riemann solver we propose herein investigates sequentially each of these configurations until an admissible solution is calculated. Special configurations, corresponding to coalescence of waves, are also analyzed and included in the solver. Further, we examine the accuracy and robustness of three known methods for the integration of the non-conservative products, via a series of numerical tests. Finally, the issue of existence and uniqueness of solutions to the Riemann problem is discussed.