FIVER: A Finite Volume Method Based on Exact Two-Phase Riemann Problems and Sparse Grids for Multi-Material Flows with Large Density Jumps

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.
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https://hal.inria.fr/hal-00703493
Contributor : Jean-Frédéric Gerbeau <>
Submitted on : Saturday, June 2, 2012 - 9:16:26 AM
Last modification on : Tuesday, May 14, 2019 - 10:16:32 AM

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Charbel Farhat, Jean-Frédéric Gerbeau, Arthur Rallu. FIVER: A Finite Volume Method Based on Exact Two-Phase Riemann Problems and Sparse Grids for Multi-Material Flows with Large Density Jumps. Journal of Computational Physics, Elsevier, 2012, 231, pp.6360-6379. ⟨10.1016/j.jcp.2012.05.026⟩. ⟨hal-00703493⟩

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