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High‐resolution finite volume computations using a novel weighted least‐squares formulation
Author(s) -
Mandal J. C.,
Rao S.,
Subramanian J.
Publication year - 2007
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.1707
Subject(s) - scalar (mathematics) , computation , conservation law , mathematics , least squares function approximation , finite volume method , algorithm , resolution (logic) , mathematical optimization , calculus (dental) , mathematical analysis , computer science , geometry , statistics , physics , artificial intelligence , estimator , mechanics , medicine , dentistry
High‐resolution finite volume schemes based on a novel reconstruction technique, SDWLS (solution‐dependent weighted least squares) are considered. The SDWLS technique, originally developed for second‐order variable reconstruction by Mandal and Subramanian ( Appl. Numer. Math. , 2007; DOI: 10.1016/j.apnum.2007.02.003 ), is further extended to third‐order reconstruction with compact stencils involving only the nearest neighbors. The new schemes are applied to solve a few numerical test examples, involving scalar conservation laws and the system of non‐linear gas dynamics equations, in order to study their performance. Significant improvements in solution accuracy have been achieved with the second‐ and third‐order SDWLS reconstruction techniques. Copyright © 2007 John Wiley & Sons, Ltd.