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Adaptive grid generation by minimizing residuals
Author(s) -
Roe Philip,
Nishikawa Hiroaki
Publication year - 2002
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.336
Subject(s) - airfoil , residual , grid , minification , mathematics , quadrature (astronomy) , mathematical optimization , computer science , algorithm , geometry , engineering , mechanics , physics , electrical engineering
We describe recent developments in the method of fluctuation splitting, in particular the minimization of residuals with respect to both the nodal values of the solution and also the nodal co‐ordinates. For elliptic problems, including external (lifting) flows, obtaining good results requires that the residuals be evaluated to third order. Solutions to typical airfoil problems can then be obtained with very economical grids. For hyperbolic problems, only a second‐order evaluation of the residual is needed. Shocks can be incorporated with arbitrarily high resolution by allowing elements to shrink to zero area, but to exclude the possibility of rarefaction shocks an adaptive quadrature must be employed. Copyright © 2002 John Wiley & Sons, Ltd.