Adaptively Refined Cartesian Grid Generation and Euler Flow Solutions for Arbitrary Geometries

An automatic Cartesian grid generator is presented together with Euler solutions of flows around complicated geometries. The computational grid is generated based on an octree-data structure. Solid bodies merely blank out areas of the background Cartesian grid. The part of the surface-intersecting cells is cut off, which lies inside the body. As a result arbitrarily shaped cut-cells arise around the geometry. The remaining cells inside the flow field benefit from their regular cubic shape. The strategy developed for the grid generation prevents numerical instabilities and treats geometric degeneracies in a generic way. Thus, cut-cells of too small size are merged into appropriate neighbour cells to ensure numerical stability of the flow solver. Two different flow solvers are applied for the Euler equations: the first solver represents a novel multi-grid upwind flow solver, which benefits directly from the octree-data structure. The second flow solver is a modified unstructured solver of Jameson type. The parameters of the adaptation criterion are calculated for every cell, thus cells are identified for adaptive refinement or coarsening.