A Quadtree-based adaptive Cartesian/Quad grid flow solver for Navier-Stokes equations

Abstract

Quadtree-based adaptive Cartesian/Quad (quadrilateral) grid generator, grid adaptor and flow solver have been developed and fully demonstrated in this study. Given the definition of geometries (cubic B-splines and straight line segments), geometrically-adaptive, body-fitted Quad grids are generated automatically. These grids are then overlapped with a large Cartesian cell which is sub-divided 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 final computational grid is then automatically produced through cell cutting. A Quadtree data structure has been used to store the grids. As a result, grid refinement and coarsening are trivial to accomplish. A cell-centered, second-order accurate viscous flow solver has been developed. The flow 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 flow solver into an automated computing environment to achieve maximum efficiency and accuracy with minimum human and computer resources.