On uniformly high-order accurate residual distribution schemes for advection-diffusion.

Mario Ricchiuto; N. Villedieu; Remi Abgrall; H. Deconinck

inria-00403700, version 1

On uniformly high-order accurate residual distribution schemes for advection-diffusion.

Mario Ricchiuto ^1, 2, N. Villedieu ³, Remi Abgrall () ^1, 2, H. Deconinck ³

Journal of Computational and Applied Mathematics 215, 2 (2008) 547-556

Abstract: We discuss preliminary results on the construction of uniformly high-order residual distribution $(\cal RD)$ type discretizations for steady advection-diffusion on unstructured grids. A properly designed scaling of the $(\cal RD)$ upwind stabilization with the physical viscosity allows to obtain schemes with uniform and arbitrary accuracy, on a very compact stencil. Second- and third-order examples are given to illustrate the potential of the approach.

1: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
2: SCALAPPLIX (INRIA Bordeaux - Sud-Ouest)
INRIA – CNRS : UMR5466 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)
3: von Karman Institute for Fluid Dynamics (VKI)
NATO

inria-00403700, version 1
http://hal.inria.fr/inria-00403700
oai:hal.inria.fr:inria-00403700
From: Rémi Abgrall <>
Submitted on: Sunday, 12 July 2009 22:37:25
Updated on: Monday, 13 July 2009 11:16:39

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DOI: 10.1016/j.cam.2006.03.059

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