A Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants

作者：Karni Smadar^*; Hernandez Duenas Gerardo

来源：Journal of Scientific Computing, 2010, 45(1-3): 382-403.

DOI：10.1007/s10915-009-9332-y

• Hyperbolic conservation laws
• Multiphase flow
• Riemann invariants

The paper considers the Baer-Nunziato model for two-phase flow in porous media, with discontinuous porosity. Computing solutions of the Riemann problem rests on capturing the jump in the solution across the porosity jump. A recent study (Lowe in J. Comput. Phys. 204:598-632, 2005) showed that numerical discretizations may fail to correctly capture the jump conditions across the so-called compaction wave, and yield incorrect solutions. We have formulated the Baer-Nunziato system using the Riemann invariants across the porosity jump, and propose a hybrid algorithm that uses the Riemann invariants formulation across the compaction wave, and the conservative formulation away from the compaction wave. The paper motivates and describes the hybrid scheme and present numerical results.