Computation Of Flows with Shocks Using Spectral Difference Scheme with Artificial Viscosity

The current work focuses on applying an arti cial viscosity approach to the Spectral Di erence (SD) method to enable high-order computation of compressible uid ows with discontinuities. The study modi es the arti cial viscosity approach proposed in the earlier work. Studies show that a dilatation sensor for arti cial viscosity, combined with a dilatation-based switch and lter for smoothing, works well for curvilinear and unstructured grids. The arti cial viscosity model is found to stabilize numerical calculations and reduce oscillations near discontinuities. Promising results are demonstrated for 2-D test problems. Adaptive mesh re nement is used in conjunction with arti cial viscosity to obtain improved shock pro les. A mortar element method is used to handle the non-conforming interfaces generated from mesh-re nement of quadrilateral elements.