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Mixed boundary elements for laminar flows
Author(s) -
Ramšak Matjaž,
Škerget Leopold
Publication year - 1999
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(19991115)31:5<861::aid-fld900>3.0.co;2-s
Subject(s) - mathematics , interpolation (computer graphics) , mathematical analysis , finite element method , boundary value problem , boundary (topology) , solver , laminar flow , geometry , mathematical optimization , physics , mechanics , classical mechanics , thermodynamics , motion (physics)
This paper presents a mixed boundary element formulation of the boundary domain integral method (BDIM) for solving diffusion–convective transport problems. The basic idea of mixed elements is the use of a continuous interpolation polynomial for conservative field function approximation and a discontinuous interpolation polynomial for its normal derivative along the boundary element. In this way, the advantages of continuous field function approximation are retained and its conservation is preserved while the normal flux values are approximated by interpolation nodal points with a uniquely defined normal direction. Due to the use of mixed boundary elements, the final discretized matrix system is overdetermined and a special solver based on the least squares method is applied. Driven cavity, natural and forced convection in a closed cavity are studied. Driven cavity results at Re =100, 400 and 1000 agree better with the benchmark solution than Finite Element Method or Finite Volume Method results for the same grid density with 21×21 degrees of freedom. The average Nusselt number values for natural convection 10 3 ≤ Ra ≤10 6 agree better than 0.1% with benchmark solutions for maximal calculated grid densities 61×61 degrees of freedom. Copyright © 1999 John Wiley & Sons, Ltd.