Open AccessHybrid Explicit Residual Distribution Scheme for Compressible Multiphase Flows
Author(s) -
Paola Bacigaluppi,
Rémi Abgrall,
Tülin Kaman
Publication year - 2017
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/821/1/012007
Subject(s) - classification of discontinuities , mathematics , compressible flow , context (archaeology) , compressibility , residual , convergence (economics) , riemann problem , flow (mathematics) , mathematical analysis , riemann hypothesis , geometry , physics , mechanics , algorithm , paleontology , economics , biology , economic growth
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. © Published under licence by IOP Publishing Ltd