High-order adaptive quadrature-free spectral volume method on unstructured grids

The high-order quadrature-free spectral volume (SV) method is extended to handle local adaptive hp-refinement (grid and order refinement). Efficient edge-based adaptation utilizing a binary tree search algorithm is employed. An adaptation criteria is selected which focuses computational effort near discontinuities, and effectively reduces the physical area of the domain necessitating data limiting for stability. This makes the method very well suited for capturing and preserving discontinuities with high resolution. Both h- and p-refinement are presented in a general framework where it is possible to perform either or both on any grid cell at any time. Several well-known inviscid flow test cases, subjected to various levels of adaptation, are utilized to demonstrate the effectiveness of the method.