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Towards generalization and optimization of implicit methods
Author(s) -
Lin Avi
Publication year - 1985
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.1650050406
Subject(s) - mathematics , partial differential equation , generalization , convergence (economics) , algebraic number , rate of convergence , computational fluid dynamics , flow (mathematics) , mathematical optimization , calculus (dental) , mathematical analysis , computer science , geometry , computer network , channel (broadcasting) , physics , mechanics , economics , economic growth , medicine , dentistry
A general implicit (GI) method for solving iteratively the algebraic system arising from a finite difference approximation of an elliptic partial differential equation is formulated. Under certain assumptions this method can be reduced to the already known implicit techniques. It is shown that the GI method has a very special physical meaning when solving fluid flow problems. It is shown also how this method can be optimized to achieve the maximum rate of convergence. Finally it is shown how this new strategy is applied by solving some classical numerical fluid dynamics problems.