Runge–Kutta discontinuous Galerkin method for Baer–Nunziato model with ‘simple WENO’ limiting of conservative variables-Reference-Cited by-同舟云学术

Runge–Kutta discontinuous Galerkin method for Baer–Nunziato model with ‘simple WENO’ limiting of conservative variables

Published:2021-04-01 Issue:2 Volume:36 Page:57-74
ISSN:1569-3988
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Alekseev Mikhail¹,Savenkov Evgeny¹

Affiliation:

1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences , Moscow 125047 , Russia

Abstract

Abstract The work is devoted to the application of Runge–Kutta discontinuous Galerkin (RKDG) method for solving Baer–Nunziato hyperbolic model for nonequilibrium two-phase flows. The approach is based on the application of the simple WENO limiter directly to the conservative variables. Mathematical model and the corresponding numerical algorithm are described. The results of numerical simulations for 1D and 2D tests are presented and discussed.

Publisher

Walter de Gruyter GmbH

Subject

Modelling and Simulation,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2021-0006/pdf

Reference33 articles.

1. N. Andrianov and G. Warnecke, The Riemann problem for the Baer–Nunziato two-phase flow model. J. Comput. Phys. 195 (2004), No. 2, 434–464.

2. M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiph. Flow 12 (1986), 861–889.

3. D. Balsara, M. Dumbser, and R. Abgrall, Multidimensional HLLC Riemann solver for unstructured meshes with application to Euler and MHD flows. J. Comput. Phys. 261 (2014), 172–208.

4. P. Barton, D. Drikakis, E. Romenski, and V. A. Titarev, Exact and approximate solutions of Riemann problems in non-linear elasticity. J. Comput. Phys. 228 (2009), No. 18, 7046–7068.

5. M. Castro, P. LeFloch, M. Munoz-Ruiz, and C. Parés, Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes. J. Comput. Phys. 227 (2008), No. 17, 8107–8129.