| A novel anisotropic adaptive mesh refinement (AMR) technique is proposed and de- scribed. A block-based AMR approach is used which permits highly efficient and scalable implementations on parallel computer architectures and the use of multi-block, body-fitted computational grids for the treatment of complex geometries. However, rather than adopting the more usual isotropic approach to the refinement of the grid blocks, the proposed approach uses a binary hierarchical tree data structure that allows for anisotropic refinement of the grid blocks in each of the coordinate directions in an inde- pendent fashion. This allows for more efficient and accurate treatment of narrow layers, discontinuities, and/or shocks in the solutions which occur, for example, in the thin boundary and mixing layers of high-Reynolds-number viscous flows and in the regions of strong non-linear wave interactions of high-speed compressible flows with shocks. The anisotropic AMR technique is implemented within an existing finite-volume framework, which encompasses both explicit and implicit solution methods, and is capable of per- forming calculations with both second- and higher-order spatial accuracy. To clearly demonstrate the potential and feasibility of the proposed AMR technique, it is applied to the unsteady and steady-state solutions of both a model system, the advection diffusion equation, as well as the Euler equations governing compressible, inviscid, gaseous flows, both in two space dimensions. |
