Study of the 2D laminar flapping wing case using the Spectral Difference method

We further developed a 2D spectral difference (SD) method code published in [1] and [2] to handle moving and deformable grids. The code is written using the spectral difference method where the solution points and flux points are arranged in a staggered fashion. We typically conduct computations using either 3rd-, 4th-, 5th-, or 6th-order SD method. The flow field within each cell is reconstructed with a smooth representation using a tensor-product form. The discontinuity across cell interfaces is handled using a Rusanov flux (Local Lax Friedrichs method). We also implemented a p-multigrid scheme for this solver. For this abstract, all results are obtained using a single-level grid with the 5rd-order SD emthod. The mesh deformation and translation are controlled using a blended function as suggested in [3] and adopted in [4]. The current form of implementation for moving and deformable grid has similarity with the one reported in [5]. Consider unsteady conservation laws only in 2D conservative form