A high-order spectral difference method for unstructured dynamic grids

Abstract

A high-order spectral difference (SD) method has been further extended to solve the three dimensional compressible Navier–Stokes (N–S) equations on deformable dynamic meshes. In the SD method, the solution is approximated with piece-wise continuous polynomials. The elements are coupled with common Riemann fluxes at element interfaces. The extension to deformable elements necessitates a time-dependent geometric transformation. The Geometric Conservation Law (GCL), which is introduced in the time-dependent transformation from the physical domain to the computational domain, has been discussed and implemented for both explicit and implicit time marching methods. Accuracy studies are performed with a vortex propagation problem, demonstrating that the spectral difference method can preserve high-order accuracy on deformable meshes. Further applications of the method to several moving boundary problems including bio-inspired flow problems are shown in the paper to demonstrate the capability of the developed method.