A high-order spectral difference method for unstructured dynamic grids

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. (C) 2011 Elsevier Ltd. All rights reserved.