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HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow. (English) Zbl 1391.76440
Summary: We first construct an approximate Riemann solver of the HLLC-type for the Baer-Nunziato equations of compressible two-phase flow for the “subsonic” wave configuration. The solver is fully nonlinear. It is also complete, that is, it contains all the characteristic fields present in the exact solution of the Riemann problem. In particular, stationary contact waves are resolved exactly. We then implement and test a new upwind variant of the path-conservative approach; such schemes are suitable for solving numerically nonconservative systems. Finally, we use locally the new HLLC solver for the Baer-Nunziato equations in the framework of finite volume, discontinuous Galerkin finite element and path-conservative schemes. We systematically assess the solver on a series of carefully chosen test problems.

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76T10 Liquid-gas two-phase flows, bubbly flows
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
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