Premium
Towards very high‐order accurate schemes for unsteady convection problems on unstructured meshes
Author(s) -
Abgrall R.,
Andrianov N.,
Mezine M.
Publication year - 2005
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.870
Subject(s) - polygon mesh , scalar (mathematics) , mathematics , residual , finite element method , advection , space (punctuation) , class (philosophy) , mathematical optimization , computer science , geometry , algorithm , physics , artificial intelligence , thermodynamics , operating system
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. Copyright © 2005 John Wiley & Sons, Ltd.