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Hybrid explicit residual distribution scheme for compressible multiphase flows


Bacigaluppi, Paola; Abgrall, Rémi; Kaman, Tulin (2017). Hybrid explicit residual distribution scheme for compressible multiphase flows. Journal of Physics : Conference Series, 821(1):012007.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:7 April 2017
Deposited On:09 Oct 2017 16:21
Last Modified:09 Oct 2017 16:21
Publisher:IOP Publishing
ISSN:1742-6588
Additional Information:1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion and Power, NICFD 2016; Villa MonasteroVarenna; Italy; 20 October 2016 through 21 October 2016; Code 127150
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1088/1742-6596/821/1/012007

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