Mixed boundary elements for laminar flows

This paper presents a mixed boundary element formulation of the boundary do main integral method (BDIM) for solving diffusion-convective transport prob lems. The basic idea of mixed elements is the use of a continuous interpola tion polynomial for conservative field function approximation and a discont inuous interpolation polynomial for its normal derivative along the boundar y element. In this way, the advantages of continuous field function approxi mation are retained and its conservation is preserved while the normal flux values are approximated by interpolation nodal points with a uniquely defi ned normal direction. Due to the use of mixed boundary elements, the final discretized matrix system is overdetermined and a special solver based on t he least squares method is applied. Driven cavity, natural and forced conve ction in a closed cavity are studied. Driven cavity results at Re = 100, 40 0 and 1000 agree better with the benchmark solution than Finite Element Met hod or Finite Volume Method results for the same grid density with 21 x 21 degrees of freedom. The average Nusselt number values for natural convectio n 10(3) less than or equal to Ra less than or equal to 10(6) agree better t han 0.1% with benchmark solutions for maximal calculated grid densities 61 x 61 degrees of freedom. Copyright (C) 1999 John Wiley & Sons, Ltd.