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Mathematics > Analysis of PDEs

arXiv:1802.04590 (math)
[Submitted on 13 Feb 2018]

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

Authors:David Coulette (TONUS, IRMA), Emmanuel Franck (TONUS), Philippe Helluy (IRMA, TONUS), Michel Mehrenberger (TONUS, IRMA), Laurent Navoret (IRMA, TONUS)
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Abstract: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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1802.04590 [math.AP]
  (or arXiv:1802.04590v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1802.04590

Submission history

From: Philippe Helluy [view email] [via CCSD proxy]
[v1] Tue, 13 Feb 2018 12:39:59 UTC (1,358 KB)
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