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Article Dans Une Revue Computers and Fluids Année : 2019

High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

Résumé

We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and time. The construction is based on: (a) the representation of the system of conservation laws by a kinetic vectorial representation with a stiff relaxation term; (b) a matrix-free, CFL-less implicit discontinuous Galerkin transport solver; and (c) a stiffly accurate composition method for time integration. The method is validated on several one-dimensional test cases. It is then applied on two-dimensional and three-dimensional test cases: flow past a cylinder, magnetohydrodynamics and multifluid sedimentation.
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hal-01706614 , version 1 (12-02-2018)

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David Coulette, Emmanuel Franck, Philippe Helluy, Michel Mehrenberger, Laurent Navoret. High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation. Computers and Fluids, 2019, 190, pp.485--502. ⟨10.1016/j.compfluid.2019.06.007⟩. ⟨hal-01706614⟩
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