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hal-00716621, version 1

Construction of a high order Residual Distribution scheme for complex viscous flows

Remi Abgrall () 1, 2, Dante De Santis () 1, Mario Ricchiuto () a, 1, 2

Seventh International Conference on Computational Fluid Dynamics (ICCFD7) (2012)

Résumé : In this work we describe the use of the Residual Distribution schemes applied to the discretization of conservation laws. In particular, emphasis is put on the construction of a third order accurate scheme. We first recall the properties of a Residual Distribution scheme and we show how to construct a high order scheme for advection problems. Furthermore, we show how to speed up the convergence of the implicit scheme to the steady solution by the means of the Jacobian-free technique. We then extend the scheme to the case of advection-diffusion problems. In particular, we propose a new approach in which the residuals of the advection and diffusion terms are distributed together to get high order accuracy. Due to the continuous approximation of the solution, the gradients of the variables are reconstructed at the nodes and then interpolated on the elements. The numerical scheme is used to discretize the advection-diffusion scalar problem and the compressible Navier-Stokes equations.

  • a –  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
  • Domaine : Sciences de l'ingénieur/Mécanique/Mécanique des fluides
    Physique/Mécanique/Mécanique des fluides
    Mathématiques/Equations aux dérivées partielles
    Mathématiques/Analyse numérique
  • Mots-clés : Navier-Stokes equations – High order schemes – Residual distribution – Computational Fluid Dynamics
 
  • hal-00716621, version 1
  • http://hal.inria.fr/hal-00716621
  • oai:hal.inria.fr:hal-00716621
  • Contributeur : Dante De Santis <>
  • Soumis le : Mardi 10 Juillet 2012, 23:55:11
  • Dernière modification le : Mardi 21 Août 2012, 10:39:03