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Published December 10, 2006 | public
Journal Article

Implementation of WENO Schemes in Compressible Multicomponent Flow Problems

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.

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.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023