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.