Implementation of Adaptive Mesh Refinement in an Implicit Unstructured Finite-Volume Flow Solver

摘要

This paper explores the implementation of adaptive mesh refinement in an implicit unstructured finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A refinement metric using a simple sensor based on undivided differences is discussed and applied to a model problem with practical applications: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties and future work prepare this method for additional research. The potential for this approach in more complicated flows is described.