Artificial Viscosity Discontinuous Galerkin Spectral Element Method for the Baer-Nunziato Equations
This paper is devoted to the numerical discretization of the hyperbolic two-phase flow model of Baer and Nunziato. Special attention is paid to the discretization of interface flux functions in the framework of Discontinuous Galerkin approach, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. A discretization scheme is proposed in a Discontinuous Galerkin framework following the criterion of Abgrall. A stabilization technique based on artificial viscosity is applied to the high-order Discontinuous Galerkin method and tested on a bench of discontinuous test cases.
This work has been partially supported by REPSOL under the research grant P130120150 monitored by Dr. Angel Rivero. This work has been partially supported by Ministerio de Economía y Competitividad (Spain) under the research grant TRA2015-67679-C2-2-R. The authors would like to thank the anonymous reviewers for their comments and suggestions which greatly improved this work.
- 4.B. Baldwin, R. MacCormack, Interaction of strong shock wave with turbulent boundary layer, in Proceedings of the Fourth International Conference on Numerical Methods in Fluid Dynamics (Springer, Berlin, 1975), pp. 51–56Google Scholar
- 10.J. Douglas, T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, in Computing Methods in Applied Sciences (Springer, Berlin, 1976), pp. 207–216Google Scholar
- 17.A. Jameson, W. Schmidt, E. Turkel, Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes, in 14th fluid and Plasma Dynamics Conference (1981), p. 1259Google Scholar
- 25.P.O. Persson, J. Peraire, Sub-cell shock capturing for discontinuous Galerkin methods, in Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2006-112 (2006)Google Scholar
- 27.W.H. Reed, T.R. Hill, Triangular mesh methods for the neutron transport equation. Los Alamos Report LA-UR-73-479 (1973)Google Scholar
- 33.E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction (Springer, Berlin, 2009)Google Scholar