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A boundary element formulation using the simple method
Author(s) -
Grigor'Ev M. M.
Publication year - 1993
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.1650160702
Subject(s) - boundary element method , discretization , mathematics , boundary knot method , boundary (topology) , laminar flow , singular boundary method , mathematical analysis , incompressible flow , plane (geometry) , constant (computer programming) , flow (mathematics) , boundary value problem , finite element method , geometry , mechanics , physics , computer science , thermodynamics , programming language
A new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well‐known SIMPLE algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and Spalding. 32 However, the new method demands a much larger computer strorage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two‐dimensional domain are found analytically. To preserve the stability in the iteration process, under‐relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates at Re = 20 and Re = 200, the flows in a square cavity with a moving upper lid at Re = 1 and Re = 100 and the flow in a plane channel with sudden symmetric expansion at Re =46·6.