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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
2 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
Université Bordeaux Segalen - Bordeaux 2, Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
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.
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https://hal.inria.fr/inria-00403700
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Submitted on : Sunday, July 12, 2009 - 10:37:25 PM
Last modification on : Thursday, February 11, 2021 - 2:38:02 PM

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Mario Ricchiuto, N. Villedieu, Remi Abgrall, H. Deconinck. On uniformly high-order accurate residual distribution schemes for advection-diffusion.. Journal of Computational and Applied Mathematics, Elsevier, 2008, 215 (2), pp.547-556. ⟨10.1016/j.cam.2006.03.059⟩. ⟨inria-00403700⟩

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