A Quadtree-based Adaptive Cartesian/quad Grid Flow Solver for Navier-stokes Equations

ÐQuadtree-based adaptive Cartesian/Quad (quadrilateral) grid generator, grid adaptor and ̄ow solver have been developed and fully demonstrated in this study. Given the de®nition of geometries (cubic B-splines and straight line segments), geometrically-adaptive, body-®tted Quad grids are generated automatically. These grids are then overlapped with a large Cartesian cell which is subdivided recursively until the Cartesian cells which are intersected by the outer boundaries of the Quad grids have similar grid resolutions to the Quad cells. The ®nal computational grid is then automatically produced through cell cutting. A Quadtree data structure has been used to store the grids. As a result, grid re®nement and coarsening are trivial to accomplish. A cell-centered, second-order accurate viscous ̄ow solver has been developed. The ̄ow solver supports arbitrary control volumes. Solution-based grid adaptations are carried out after converged solutions are obtained on a given grid. Grid independent inviscid and viscous solutions have been obtained through automatic grid adaptations. The overall solution procedure integrates grid generation, grid adaptation and ̄ow solver into an automated computing environment to achieve maximum eciency and accuracy with minimum human and computer resources. # 1998 Elsevier Science Ltd. All rights reserved