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A boundary element method for steady viscous fluid flow using penalty function formulation
Author(s) -
Grigoriev M. M.,
Fafurin A. V.
Publication year - 1997
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/(sici)1097-0363(19971030)25:8<907::aid-fld592>3.0.co;2-t
Subject(s) - reynolds number , mathematics , quadrilateral , discretization , boundary element method , incompressible flow , penalty method , stokes flow , mathematical analysis , compressibility , rate of convergence , boundary (topology) , vortex , quadratic equation , flow (mathematics) , finite element method , mechanics , geometry , mathematical optimization , physics , computer science , thermodynamics , channel (broadcasting) , computer network , turbulence
A new boundary element method is presented for steady incompressible flow at moderate and high Reynolds numbers. The whole domain is discretized into a number of eight‐noded cells, for each of which the governing boundary integral equation is formulated exclusively in terms of velocities and tractions. The kernels used in this paper are the fundamental solutions of the linearized Navier–Stokes equations with artificial compressibility. Significant attention is given to the numerical evaluation of the integrals over quadratic boundary elements as well as over quadratic quadrilateral volume cells in order to ensure a high accuracy level at high Reynolds numbers. As an illustration, square driven cavity flows are considered for Reynolds numbers up to 1000. Numerical results demonstrate both the high convergence rate, even when using simple (direct) iterations, and the appropriate level of accuracy of the proposed method. Although the method yields a high level of accuracy in the primary vortex region, the secondary vortices are not properly resolved. © 1997 John Wiley & Sons, Ltd.