Implementation of adaptive mesh refinement in an implicit unstructured finite-volume flow solver

This paper explores the implementation of adaptive mesh refinement in an implicit un- structured 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 eficient, 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 diff- culties and future work prepare this method for additional research. The potential for this approach in more complicated flows is described.