High-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation

This study proposes an extension of the high-order compact gas-kinetic scheme(CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian(ALE) formulation in unstructured mesh. The ALE method is achieved bysubdividing arbitrary mesh into tetrahedrons and integrating flux function in alocal coordinate system at the cell interface to ensure geometric conservationlaw. The scheme incorporates a compact reconstruction with third-order accuracyfor updating both cell-averaged conservative flow variables and theirgradients. HWENO-type nonlinear reconstruction and gradient compression factorsare adopted to improve the accuracy and robustness of the scheme. A multi-stagemulti-derivative (MSMD) time-stepping method is also implemented to achievehigh-order time accuracy with fewer middle stages. The scheme is used to studyproblems involving moving boundaries. The numerical experiments demonstrate theeffectiveness of the scheme in capturing the accurate solutions of bothlow-speed smooth flow and highly compressible ones with strong shock waves.