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On upwind methods for parabolic finite elements in incompressible flows
Author(s) -
Hendriana Dena,
Bathe KlausJürgen
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000110/30)47:1/3<317::aid-nme773>3.0.co;2-n
Subject(s) - upwind scheme , mathematics , finite element method , compressibility , galerkin method , ideal (ethics) , flow (mathematics) , incompressible flow , discontinuous galerkin method , mathematical analysis , mechanics , geometry , discretization , physics , engineering , structural engineering , philosophy , epistemology
We study the performance of various upwind techniques implemented in parabolic finite element discretizations for incompressible high Reynolds number flow. The characteristics of an ‘ideal’ upwind procedure are first discussed. Then the streamline upwind Petrov/Galerkin method, a simplified version thereof, the Galerkin least squares technique and a high‐order derivative artificial diffusion method are evaluated on test problems. We conclude that none of the methods displays the desired solution characteristics. There is still need for the development of a reliable and efficient upwind method with characteristics close to those of the ‘ideal’ procedure. Copyright © 2000 John Wiley & Sons, Ltd.