Computation of flows with shocks using the Spectral Difference method with artificial viscosity, II: Modified formulation with local mesh refinement

• Computing flows with shocks using Spectral Difference method on unstructured quad grids.
• Modified artificial viscosity formulation to use dilatation-based sensor.
• Showed improved performance on curvilinear and non-cartesian unstructured grids.
• Obtained stable and well resolved shocks for variety of problems in 2D.
• Used mortar element method to enable local mesh refinement in regions of shocks.

The current work focuses on applying an artificial viscosity (AV) approach to the Spectral Difference (SD) method to enable high-order computation of compressible fluid flows with discontinuities. The study improves on the AV approach proposed in our prior work [1] to obtain a formulation that performs better on curvilinear and non-cartesian unstructured grids. A dilatation sensor for the AV coefficient, combined with a dilatation-based switch and filter for smoothing, is found to reduce the oscillatory behavior and enable sharp capturing of discontinuities. The work also incorporates the capability for local mesh refinement, which is used in conjunction with AV to obtain improved shock profiles. A mortar element method is used to handle the non-conforming interfaces generated from mesh-refinement of quadrilateral elements. Promising results are demonstrated for 2D test problems.