Assessment of geometric multilevel convergence robustness and a wall distance method for flows with multiple internal boundaries

The two dimensional equations governing conservation of mass and momentum are solved for blocked off geometries (where control volumes are rendered inactive) relevant to electronics. Such geometries are generally characterised by many rectangular components which form numerous surfaces. For turbulent predictions, the distances from these surfaces, required in certain turbulence models, are inferred from the solution of a modified Poisson equation based algorithm. Convergence of both the Poisson and fluid flow equations are enhanced by using geometric linear and non-linear multilevel algorithms, respectively. When geometric multilevel convergence acceleration is used for turbulent flows, with blocked of regions, ideally grid lines should be fixed adjacent to solid surfaces on all grid levels. This will prevent distortion of geometry as the grid is coarsened. However,the numerous surfaces found in most realistic electronic systems makes the prevention of all geometrical distortion impractical. The feasibility of using a non-linear geometric multilevel approach, where only key geometrical elements are fixed is assessed. Also, the influence of coarse grid aspect ratio on convergence is studied. Comparisons are made with analytical and experimental velocity data for cylindrical and Cartesian geometries with laminar and turbulent flow. Satisfactory agreement is found and predicted wall distances are shown to be accurate. Results suggest that for the range of cases presented the multilevel method is reasonably resilient to geometric distortion and at worst could be used as a technique for producing good initial guesses to solutions. Also, the work indicates that low aspect ratio control volumes on coarser grid levels do not necessarily improve convergence. For the case considered a coarse grid aspect ratio of around 100:1 giving optimum convergence. (C) 1998 Elsevier Science Inc. All rights reserved.