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

Authors:
M. Ricchiuto;N. Villedieu;R. Abgrall;H. Deconinck
Affiliations:
INRIA Futurs, project ScAlApplix and Mathématiques Appliquées de Bordeaux, Université de Bordeaux I, 351 cours de la Libération, 33405 Talence cedex, France;Department of Aeronautics and aerospace, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, B-1640 Rhode-Saint-Genèse, Belgium;INRIA Futurs, project ScAlApplix and Mathématiques Appliquées de Bordeaux, Université de Bordeaux I, 351 cours de la Libération, 33405 Talence cedex, France and Institut Univer ...;Department of Aeronautics and aerospace, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, B-1640 Rhode-Saint-Genèse, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

We discuss preliminary results on the construction of uniformly high-order residual distribution (RD) type discretizations for steady advection-diffusion on unstructured grids. A properly designed scaling of the 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.