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hal-00647999, version 2

Numerical approximation of parabolic problems by means of residual distribution schemes

Remi Abgrall () 1, 2, Guillaume Baurin () 1, Arnaud Krust () a, 1, Dante De Santis b, 1, 2, Mario Ricchiuto b, 1, 2

N° RR-7824 (2011)

Abstract: We are interested in the numerical approximation of steady scalar convection diffusion problems by mean of high order schemes called Residual Distribution (RD). In the inviscid case, one can develop non linear RD that are non oscillatory, even in the case of very strong shocks, while having the most possible compact stencil, on hybrid unstructured meshes. This paper proposes and compare several extension of these schemes for the convection diffusion problem. This methodology, in particular in term of accuracy, is evaluated on several problems, some of which having exact solutions.

  • a –  INRIA Bordeaux Sud Ouest
  • b –  INRIA
  • 1:  BACCHUS (INRIA Bordeaux - Sud-Ouest)
  • INRIA – Université de Bordeaux – CNRS : UMR5800
  • 2:  Institut de Mathématiques de Bordeaux (IMB)
  • CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
  • Domain : Mathematics/Analysis of PDEs
    Engineering Sciences/Mechanics/Fluids mechanics
    Physics/Mechanics/Mechanics of the fluids
  • Keywords : Convection diffusion – residual distribution schemes – finite element methods – non structured meshes
  • Internal note : RR-7824
  • Available versions :  v1 (2011-12-05) v2 (2011-12-14)
 
  • hal-00647999, version 2
  • http://hal.inria.fr/hal-00647999
  • oai:hal.inria.fr:hal-00647999
  • From: Rémi Abgrall <>
  • Submitted on: Wednesday, 14 December 2011 12:34:07
  • Updated on: Wednesday, 14 December 2011 13:23:00