Unstructured Adaptive Mesh Refinement and Coarsening for Fluid Flow at All Speeds Using a Coupled Solver

Abstract

This paper reports on the implementation and testing of an adaptive mesh refinement and coarsening algorithm based on the hanging node technique for all speeds laminar and inviscid flow problems using a fully coupled finite volume solver. The implicit pressure‐velocity coupling is accomplished by deriving a pressure equation in a way similar to a segregated SIMPLE algorithm with the extended set of equations solved simultaneously and having diagonally dominant coefficients. Mesh adaption is triggered using adaption threshold for both refinement and coarsening processes. Refinement and coarsening are done locally without the need of an explicit history of the domain cells. The success of the mesh adaption technique is demonstrated by presenting solutions for the supersonic flow over a circular arc bump problem. Results reveal that the adaptive refinement algorithm was able to detect regions of high gradients and to capture shock waves. Moreover, the adaptive mesh coarsening was successfully able to delete cells in regions were no more needed.