HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer-Nunziato two-fluid model. (English) Zbl 1373.76136
Summary: The computation of compressible two-phase flows with the Baer-Nunziato model is addressed. Only the convective part of the model that exhibits non-conservative products is considered and the source terms of the model that represent the exchange between phases are neglected. Based on the solver proposed by S. A. Tokareva and E. F. Toro [ibid. 229, No. 10, 3573–3604 (2010; Zbl 1391.76440)], a new HLLC-type Riemann solver is built. The key idea of this new solver lies in an approximation of the two-phase contact discontinuity of the model. Thus the Riemann invariants of the wave are approximated in the “subsonic” case. A major consequence of this approximation is that the resulting solver can deal with any equation of state. It also allows to bypass the resolution of a nonlinear equation based on those Riemann invariants. We assess the solver and compare it with others on 1D Riemann problems including grid convergence and efficiency studies. The ability of the proposed solver to deal with complex equations of state is also investigated. Finally, the different solvers have been compared on challenging 2D test cases due to the presence of both material interfaces and shock waves: a shock-bubble interaction and underwater explosions. When compared with others, the present solver appears to be accurate, efficient and robust.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76N99 | Compressible fluids and gas dynamics |
| 35L40 | First-order hyperbolic systems |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
two-phase compressible flows; hyperbolic PDEs; Riemann problems; finite-volume method; HLLC solverCitations:
Zbl 1391.76440References:
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