A modified artificial viscosity for shock-capturing and its application in discontinuous Galerkin methods

To improve the performance of artificial viscosity (AV) methods in compressible multi-scale flow simulations, we aim to develop a modified AV flux with both good shock-capturing capability and adjustable low-dissipation in vortex-dominated regions. First, representative quantities for shocks and vortices are selected and dissipation equations for these quantities based on four existing AV fluxes are derived. Second, the dissipation behavior of these AV fluxes is analyzed and compared based on theoretical analysis and numerical experiments. Third, a modified AV flux is proposed by combining the existing AV fluxes, which has shock-capturing capability similar to the Laplacian form AV flux and has adjustable low-dissipation in vortex-dominated regions. Cases including shock tubes, Kelvin–Helmholtz instability, shock wave/shear-layer interaction, shock wave/boundary-layer interaction, supersonic airfoil, and high pressure turbine vane are adopted to test and compare the performance of different AV fluxes. The results show that the modified AV flux simulates shocks with relatively low numerical oscillations and captures more flow details in vortex-dominated regions, which indicates that it is promising in compressible turbulence simulations.