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Implementation of WENO Schemes in Compressible Multicomponent Flow Problems

Johnsen, Eric and Colonius, Tim (2006) Implementation of WENO Schemes in Compressible Multicomponent Flow Problems. Journal of Computational Physics, 219 (2). pp. 715-732. ISSN 0021-9991. https://resolver.caltech.edu/CaltechAUTHORS:20190718-165128280

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Abstract

High-order accurate shock-capturing schemes are capable of properly resolving discontinuities with correct wave speeds in single-fluid Riemann problems. However, when different fluids are present, oscillations develop at interfaces. A class of existing interface-capturing methods that suppress these oscillations is based on first- and second-order accurate reconstructions with Roe solvers. In this paper, we extend these methods to high-order accurate WENO schemes and the HLLC approximate Riemann solver. In particular, we show that a finite volume formulation where the appropriately averaged primitive variables are reconstructed leads to the oscillation-free advection of an isolated interface. Furthermore, numerical experiments show no spurious oscillations for problems where shockwaves and interfaces interact. We solve the Euler equations supplemented by a stiffened equation of state to model flows of gas and liquid components. Our method is high-order accurate, quasi-conservative, shock-capturing and interface-capturing; these properties are additionally verified by considering one-dimensional multicomponent Riemann problems and a two-dimensional shock–bubble interaction.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jcp.2006.04.018DOIArticle
https://www.sciencedirect.com/science/article/pii/S0021999106002014PublisherArticle
ORCID:
AuthorORCID
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2006 Elsevier. Received 29 July 2005; received in revised form 7 April 2006; accepted 12 April 2006; available online 21 June 2006. The authors wish to thank Randall LeVeque and Ralf Deiterding for helpful conversations. This work was supported by NIH Grant PO1 DK043881.
Funders:
Funding AgencyGrant Number
NIHPO1 DK043881
Subject Keywords:Multicomponent flows, WENO, HLLC solver,Interface capturing, Interface oscillations, Shock–bubble interaction
Issue or Number:2
Record Number:CaltechAUTHORS:20190718-165128280
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190718-165128280
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97278
Collection:CaltechAUTHORS
Deposited By: Melissa Ray
Deposited On:26 Jul 2019 18:16
Last Modified:03 Oct 2019 21:30

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