HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow

• Published in: Journal of computational physics Vol. 229; no. 10; pp. 3573 - 3604
• Main Authors: Tokareva, S.A., Toro, E.F.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.05.2010; Elsevier
• Subjects: Approximation; Complete Riemann solvers; Compressible multiphase flow; Computational techniques; Contact; DG finite elements; Exact sciences and technology; Exact solutions; Finite element method; Finite volumes; Galerkin methods; HLLC solver; Hyperbolic equations; Mathematical analysis; Mathematical methods in physics; Nonconservative products; Path-conservative methods; Physics; Riemann solver; Solvers; Path-conservative methods; DG finite elements; Hyperbolic equations; Nonconservative products; HLLC solver; Finite volumes; Complete Riemann solvers; Compressible multiphase flow; Multiphase flow; Riemann problem; Non conservative system; Calculation methods; Exact solution; Two-phase flow; Calculation; Compressible flow
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.01.016

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.