Parallel Anisotropic Block-Based Adaptive Mesh Refinement Algorithm For Three-Dimensional Flows A three-dimensional, parallel, anisotropic, block-based, adaptive mesh refinement (AMR) algorithm is proposed and described for the solution of fluid flows on bodyfitted, multi-block, hexahedral meshes. Refinement and de-refinement in any grid block computational direction, or combination of directions, allows the mesh to rapidly adapt to anisotropic flow features such as shocks, boundary layers, or

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... lame fronts, common to complex flow physics. Anisotropic refinements and an efficient and highly scalable parallel implementation lead to a potential for significant reduction in computational cost as compared to a more typical isotropic approach. Unstructured root-block topology allows for greater flexibility in the treatment of complex geometries. The AMR algorithm is coupled with an upwind finite-volume scheme for the solution of the Euler equations governing inviscid, compressible, gaseous flow. Steady-state and time-varying, three-dimensional, flow problems are investigated for various geometries, including the cubed-sphere mesh. ii