Anisotropic Non-Uniform Block-Based Adaptive Mesh Refinement for Three-Dimensional Inviscid and Viscous Flows

Abstract

A parallel anisotropic block-based adaptive mesh refinement (AMR) algorithm is proposed to describe the solution of physically complex flow problems with disparate spatial and temporal scales exhibiting highly anisotropic features on three-dimensional multi-block body-fitted hexahedral meshes with non-uniform grid blocks. Instead of using a classical uniform treatment for the computational cells of each block within the multi-block grids, the proposed anisotropic AMR scheme adopts a non-uniform representation of the cells within each block. With the former approach, all of the cells for a given block are forced to be at the same resolution, including both interior and ghost cells containing solution information from neighboring blocks. In such a uniform representation, various techniques are required to evaluate the solution in the ghost cells and ensure flux conservation at block interfaces with such a uniform representation. The proposed non-uniform approach directly uses the neighboring cells as the ghost cells, even at a grid resolution change, and this affords a number of computational advantages. A modified upwind 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 flow. Steady-state and time-varying flow problems are considered on anisotropic adapted meshes. The potential flexibility and efficiency of this enhanced anisotropic AMR scheme are demonstrated for the simulation of flows of varying complexity.