A parallel, anisotropic, block-based, adaptive mesh refinement (AMR) algorithm is proposed and described for the solution of physically complex flow problems with both highly disparate and anisotropic spatial scales and flow features on three-dimensional, multi-block, body-fitted, hexahedral meshes. The block-based AMR is used to allow local refinement of the mesh and for its efficient and highly scalable parallel implementation. The body-fitted hexahedral grid blocks with unstructured root block topology and connectivity are used to afford the treatment of complex geometries. Instead of using more traditional isotropic mesh refinement strategies, the proposed AMR scheme uses a binary tree hierarchical data structure to permit anisotropic refinement of the grid blocks in a preferred coordinate direction as dictated by appropriately selected physics-based refinement criteria. The anisotropic coarsening of the grid blocks in a manner that is independent of the refinement history allows the mesh to rapidly re-adapt for unsteady flow applications. Overall, the proposed anisotropic AMR procedure allows for more efficient and accurate capturing of complex flow features such as shocks, boundary layers, or flame fronts. The AMR scheme is applied in conjunction with an upwind finite-volume spatial discretization scheme to the solution of the Euler equations for inviscid compressible gaseous flow. Steady-state and time-varying flow problems are considered on anisotropic adapted meshes. Anisotropic adapted cubed-sphere grids are investigated. The potential of anisotropic AMR for simulation of complex flows in an efficient and generalized manner is demonstrated.
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