Hybrid Explicit Residual Distribution Scheme for Compressible Multiphase Flows

[摘要] The aim of this work is the development of a fully explicit scheme in the framework of time dependent hyperbolic problems with strong interacting discontinuities to retain high order accuracy in the context of compressible multiphase flows. A new methodology is presented to compute compressible two-fluid problems applied to the five equation reduced model given in Kapila et al. (Physics of Fluids 2001). With respect to other contributions in that area, we investigate a method that provides mesh convergence to the exact solutions, where the studied non-conservative system is associated to consistent jump relations. The adopted scheme consists of a coupled predictor-corrector scheme, which follows the concept of residual distributions in Ricchiuto and Abgrall (J. Comp. Physics 2010), with a classical Glimm's scheme (J. Sci. Stat. Comp. 1982) applied to the area where a shock is occurring. This numerical methodology can be easily extended to unstructured meshes. Test cases on a perfect gas for a two phase compressible flow on a Riemann problem have verified that the approximation converges to its exact solution. The results have been compared with the pure Glimm's scheme and the expected exact solution, finding a good overlap.

[发布机构] Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, Zürich; CH-8057, Switzerland^1

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] High-order accuracy;Hyperbolic problems;Non conservative systems;Numerical methodologies;Predictor-corrector schemes;Residual distribution;Residual distribution schemes;Unstructured meshes