R-adaptive Mesh Algorithms with High-order Flux Reconstruction Scheme for High-speed Flows

The present paper addresses the development and implementation of the first r-adaptive mesh refinement (r-AMR) algorithm for a high-order Flux Reconstruction solver. The r-refinement consists of nodal re-positioning while keeping their number and connectivity constants. The developed algorithms are based on physics-driven spring-analogies, where the mesh can be seen as a network of fictitious springs. While AMR increases the local mesh density, the high-order Flux Reconstruction method potentially provides more accurate detection of complex flow features over relatively coarser mesh resolution, when compared to low-order methods. In this work, a concise overview of the Flux Reconstruction method and spring-based mesh adaptation techniques will be given, followed by some promising results of r-AMR applied to benchmark high-order supersonic flow simulations.