Computation of flows with shocks using the Spectral Difference method with artificial viscosity, I: Basic formulation and application

• Computing flows with shocks using Spectral Difference method on unstructured quad grids.
• Extended high-wave number biased artificial viscosity approach to unstructured meshes.
• Promising results with stable, well resolved discontinuities for 1D and 2D test cases.

The present work combines the Spectral Difference method with an artificial viscosity based approach to enable high-order computation of compressible fluid flows with discontinuities. The study uses an artificial viscosity approach similar to the high-wavenumber biased artificial viscosity approach (Cook and Cabot, 2005, 2004; Kawai and Lele, 2008) [1–3], extended to an unstructured grid setup. The model employs a bulk viscosity for treating shocks, a shear viscosity for treating turbulence, and an artificial conductivity to handle contact discontinuities. The high-wavenumber biased viscosity is found to stabilize numerical calculations and reduce oscillations near discontinuities. Promising results are demonstrated for 1D and 2D test problems.