Premium
A poly‐region boundary element method for incompressible viscous fluid flows
Author(s) -
Grigoriev M. M.,
Dargush G. F.
Publication year - 1999
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(19991110)46:7<1127::aid-nme746>3.0.co;2-g
Subject(s) - reynolds number , boundary element method , mathematics , finite element method , singularity , geometry , galerkin method , compressibility , inflow , mechanics , mathematical analysis , physics , thermodynamics , turbulence
A boundary element method (BEM) for steady viscous fluid flow at high Reynolds numbers is presented. The new integral formulation with a poly‐region approach involves the use of the convective kernel with slight compressibility that was previously employed by Grigoriev and Fafurin [1] for driven cavity flows with Reynolds numbers up to 1000. In order to avoid the overdeterminancy of the global set of equations when using eight‐noded rectangular volume cells from that previous work, 12‐noded hexagonal volume regions are introduced. As a result, the number of linearly independent integral equations for each node becomes equal to the degrees of freedom of the node. The numerical results for square‐driven cavity flow having Reynolds numbers up to 5000 are compared to those obtained by Ghia et al . [2] and demonstrate a high level of accuracy even in resolving the secondary vortices at the corners of the cavity. Next, a comprehensive study is done for backward‐facing step flows at Re =500 and 800 using the BEM, along with a standard Galerkin‐based finite element methods (FEM). The numerical methods are in excellent agreement with the benchmark solution published by Gartling [3]. However, several additional aspects of the problem are also considered, including the effect of the inflow boundary location and the traction singularity at the step corner. Furthermore, a preliminary comparative study of the poly‐region BEM versus the standard FEM indicates that the new method is more than competitive in terms of accuracy and efficiency. Copyright © 1999 John Wiley & Sons, Ltd.