Enhanced anisotropic block-based adaptive mesh refinement for three-dimensional inviscid and viscous compressible flows

Abstract

A parallel anisotropic block-based adaptive mesh refinement (AMR) algorithm is proposed for the prediction of physically complex flow problems having disparate spatial and temporal scales and exhibiting highly anisotropic features on three-dimensional multi-block body-fitted hexahedral meshes with non-uniform grid blocks. The proposed AMR scheme makes use of a binary tree hierarchical data structure to permit anisotropic refinement of 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 evolving unsteady flow applications. Moreover, the proposed anisotropic AMR scheme adopts a non-uniform representation of the cells within each block by directly using the neighboring cells as the ghost cells, even at a grid resolution change. This affords a number of computational advantages especially related to evaluating the solution in the ghost cells as well as to ensuring flux conservation at block interfaces. A modified upwind-based finite-volume spatial discretization scheme is applied in conjunction with the AMR scheme to the solution of Euler and Navier-Stokes equations for inviscid and viscous compressible gaseous flows. Steady-state and time-varying flow problems are considered on anisotropic adapted meshes. The potential flexibility and efficiency of the proposed enhanced anisotropic AMR scheme are demonstrated for the simulation of a number of representative flows of varying complexity.