A reconstructed discontinuous Galerkin method for compressible flows on moving curved grids

Abstract A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving deforming unstructured curved meshes. Taylor basis functions the rDG are defined time-dependent domain, where integration computations performed. The Geometric Conservation Law (GCL) satisfied by modifying grid velocity terms right-hand side of discretized equations at Gauss quadrature points. radial function (RBF) interpolation used propagating mesh motion boundary nodes to interior mesh. third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) employed temporal integration. number benchmark test cases conducted assess accuracy robustness rDG-ALE problems. numerical experiments indicate that can attain designed spatial orders accuracy, RBF effective robust avoid excessive distortion invalid elements near boundaries.