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Numerical approximation of parabolic problems by residual distribution schemes
Author(s) -
Abgrall R.,
Baurin G.,
Krust A.,
de Santis D.,
Ricchiuto M.
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3710
Subject(s) - inviscid flow , classification of discontinuities , stencil , residual , polygon mesh , mathematics , scalar (mathematics) , convection–diffusion equation , nonlinear system , mathematical optimization , mathematical analysis , geometry , mechanics , algorithm , physics , computational science , quantum mechanics
SUMMARY 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. Copyright © 2012 John Wiley & Sons, Ltd.