FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps

  • Authors:

  • Charbel Farhat;Jean-FréDéRic Gerbeau;Arthur Rallu

  • Affiliations:

  • Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035, USA and Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4035, USA and Instit ...;INRIA Paris-Rocquencourt, 78153 Le Chesnay Cedex, France and Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4035, USA;Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-4035, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

A robust finite volume method for the solution of high-speed compressible flows in multi-material domains involving arbitrary equations of state and large density jumps is presented. The global domain of interest can include a moving or deformable subdomain that furthermore may undergo topological changes due to, for example, crack propagation. The key components of the proposed method include: (a) the definition of a discrete surrogate material interface, (b) the computation of a reliable approximation of the fluid state vector on each side of a discrete material interface via the construction and solution of a local, exact, two-phase Riemann problem, (c) the algebraic solution of this auxiliary problem when the equation of state allows it, and (d) the solution of this two-phase Riemann problem using sparse grid tabulations otherwise. The proposed computational method is illustrated with the three-dimensional simulation of the dynamics of an underwater explosion bubble.