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Fluid flow analysis by finite element method using arbitrarily deformed elements (Proposal of the GMSR‐method)
Author(s) -
Matsuda Y.,
Shao C.,
Yoshino M.,
Hoshihara M.,
Tanaka Y.
Publication year - 2004
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.795
Subject(s) - finite element method , computation , galerkin method , mathematics , flow (mathematics) , stability (learning theory) , computational fluid dynamics , fluid dynamics , numerical analysis , algorithm , computer science , mathematical analysis , geometry , mechanics , physics , engineering , structural engineering , machine learning
Abstract The generalized MSR‐method (GMSR‐method) is proposed as a finite element fluid analysis algorithm for arbitrarily deformed elements using the error analysis approach. The MSR‐method was originally developed by one of the authors in our previous research works using a modified Galerkin method (MGM) for a convection–diffusion equation and the SIMPLER‐approach. In this paper, this MGM is developed theoretically in the case of arbitrarily deformed elements using the error analysis approach. In the GMSR‐method, since the inertia term and the pressure term are considered explicitly, only symmetrical matrices appear. Hence, it helps us reduce computational memory and computation time. Moreover, artificial viscosity and diffusivity are introduced through an error analysis approach to improve the accuracy and stability. This GMSR‐method is applied for two‐ and three‐dimensional natural convection problems in a cavity. In the computations at different Rayleigh numbers, it is shown that this method gives reasonable results compared to other research works. Thus, it is found that the GMSR‐method is applicable to thermal‐fluid flow problems with complicated boundaries. Copyright © 2004 John Wiley & Sons, Ltd.