Implementation of WENO schemes in compressible multicomponent flow problems

  • Authors:

  • Eric Johnsen;Tim Colonius

  • Affiliations:

  • Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States;Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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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.