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Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes.

Abstract : Summary: We construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the first class of methods, we interpolate the solution in the space-time element. We start by calculating the first-order node residuals, then we calculate the high-order cell residual, and modify the first-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order finite difference approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems.
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https://hal.inria.fr/inria-00402652
Contributor : Rémi Abgrall <>
Submitted on : Tuesday, July 7, 2009 - 10:43:11 PM
Last modification on : Thursday, January 11, 2018 - 6:21:22 AM

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R. Abgrall, N. Andrianov, M. Mezine. Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes.. International Journal for Numerical Methods in Fluids, Wiley, 2005, 47 (8-9), pp.679-691. ⟨10.1002/fld.870⟩. ⟨inria-00402652⟩

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