Abstract
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.
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Work supported in part by NSF DMS #0609766 and by CONACYT #160147.
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Karni, S., Hernández-Dueñas, G. A Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants. J Sci Comput 45, 382–403 (2010). https://doi.org/10.1007/s10915-009-9332-y
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DOI: https://doi.org/10.1007/s10915-009-9332-y