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

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 56 articles , 2 standard articles )

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  1. Alekseev, Mikhail; Savenkov, Evgeny: Runge-Kutta discontinuous Galerkin method for Baer-Nunziato model with `simple WENO’ limiting of conservative variables (2021)
  2. Korneev, B. A.; Tukhvatullina, R. R.; Savenkov, E. B.: Numerical investigation of two-phase hyperbolic models (2021)
  3. Hennessey, M.; Kapila, A. K.; Schwendeman, D. W.: An HLLC-type Riemann solver and high-resolution Godunov method for a two-phase model of reactive flow with general equations of state (2020)
  4. Kemm, Friedemann; Gaburro, Elena; Thein, Ferdinand; Dumbser, Michael: A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model (2020)
  5. Serezhkin, Alexey; Menshov, Igor: On solving the Riemann problem for non-conservative hyperbolic systems of partial differential equations (2020)
  6. Toro, E. F.; Saggiorato, B.; Tokareva, S.; Hidalgo, A.: Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form (2020)
  7. Daude, F.; Berry, R. A.; Galon, P.: A finite-volume method for compressible non-equilibrium two-phase flows in networks of elastic pipelines using the Baer-Nunziato model (2019)
  8. Demay, Charles; Bourdarias, Christian; de Meux, Benoît de Laage; Gerbi, Stéphane; Hérard, Jean-Marc: A splitting method adapted to the simulation of mixed flows in pipes with a compressible two-layer model (2019)
  9. Hyde, David A. B.; Fedkiw, Ronald: A unified approach to monolithic solid-fluid coupling of sub-grid and more resolved solids (2019)
  10. Renac, Florent: Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows (2019)
  11. Saleh, Khaled: A relaxation scheme for a hyperbolic multiphase flow model. I: Barotropic EOS (2019)
  12. Serezhkin, A.: Mathematical modeling of wide-range compressible two-phase flows (2019)
  13. Denner, Fabian; Xiao, Cheng-Nian; van Wachem, Berend G. M.: Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation (2018)
  14. Fechter, Stefan; Munz, Claus-Dieter; Rohde, Christian; Zeiler, Christoph: Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension (2018)
  15. Pelanti, Marica: Wave structure similarity of the HLLC and Roe Riemann solvers: application to low Mach number preconditioning (2018)
  16. Prebeg, Marin; Flåtten, Tore; Müller, Bernhard: Large time step HLL and HLLC schemes (2018)
  17. Verma, Prabal Singh; Müller, Wolf-Christian: Higher order finite volume central schemes for multi-dimensional hyperbolic problems (2018)
  18. Boscheri, Walter: High order direct arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes for hyperbolic systems on unstructured meshes (2017)
  19. Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled: A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model (2017)
  20. ten Eikelder, M. F. P.; Daude, F.; Koren, B.; Tijsseling, A. S.: An acoustic-convective splitting-based approach for the Kapila two-phase flow model (2017)

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