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Solution of the Navier–Stokes equations in velocity–vorticity form using a Eulerian–Lagrangian boundary element method
Author(s) -
Young D. L.,
Yang S. K.,
Eldho T. I.
Publication year - 2000
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 - 10.1002/1097-0363(20001215)34:7<627::aid-fld78>3.0.co;2-j
Subject(s) - vorticity , vorticity equation , mathematics , navier–stokes equations , eulerian path , boundary element method , vector field , conservative vector field , mathematical analysis , stokes drift , incompressible flow , finite element method , classical mechanics , flow (mathematics) , mechanics , vortex , physics , compressibility , geometry , lagrangian , wave propagation , quantum mechanics , thermodynamics
This paper describes the Eulerian–Lagrangian boundary element model for the solution of incompressible viscous flow problems using velocity–vorticity variables. A Eulerian–Lagrangian boundary element method (ELBEM) is proposed by the combination of the Eulerian–Lagrangian method and the boundary element method (BEM). ELBEM overcomes the limitation of the traditional BEM, which is incapable of dealing with the arbitrary velocity field in advection‐dominated flow problems. The present ELBEM model involves the solution of the vorticity transport equation for vorticity whose solenoidal vorticity components are obtained iteratively by solving velocity Poisson equations involving the velocity and vorticity components. The velocity Poisson equations are solved using a boundary integral scheme and the vorticity transport equation is solved using the ELBEM. Here the results of two‐dimensional Navier–Stokes problems with low–medium Reynolds numbers in a typical cavity flow are presented and compared with a series solution and other numerical models. The ELBEM model has been found to be feasible and satisfactory. Copyright © 2000 John Wiley & Sons, Ltd.