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Numerical approximation of parabolic problems by residual distribution schemes


Abgrall, Rémi; Baurin, G; Krust, Arnaud; de Santis, Dante; Ricchiuto, Mario (2013). Numerical approximation of parabolic problems by residual distribution schemes. International Journal for Numerical Methods in Fluids, 71(9):1191-1206.

Abstract

We are interested in the numerical approximation of steady scalar convection-diffusion problems by means of high order schemes called Residual Distribution schemes. In the inviscid case, one can develop nonlinear Residual Distribution schemes that are nonoscillatory, even in the case of very strong discontinuities, while having the most possible compact stencil, on hybrid unstructured meshes. This paper proposes and compare extensions of these schemes for the convection-diffusion problem. This methodology, in particular in terms of accuracy, is evaluated on problem with exact solutions. Its nonoscillatory behavior is tested against the Smith and Hutton problem.

Abstract

We are interested in the numerical approximation of steady scalar convection-diffusion problems by means of high order schemes called Residual Distribution schemes. In the inviscid case, one can develop nonlinear Residual Distribution schemes that are nonoscillatory, even in the case of very strong discontinuities, while having the most possible compact stencil, on hybrid unstructured meshes. This paper proposes and compare extensions of these schemes for the convection-diffusion problem. This methodology, in particular in terms of accuracy, is evaluated on problem with exact solutions. Its nonoscillatory behavior is tested against the Smith and Hutton problem.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2013
Deposited On:21 Nov 2013 09:27
Last Modified:05 Apr 2016 17:10
Publisher:Wiley-Blackwell
ISSN:0271-2091
Publisher DOI:https://doi.org/10.1002/fld.3710

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