Scalar and Directional Localized Artificial Diffusivity Methods to Capture Shock–Turbulence Interaction

The local artificial diffusivity (LAD)-based methods rely on adding a grid-dependent artificial fluid transport coefficient (shear viscosity, bulk viscosity, and thermal diffusivity) to the physical fluid transport coefficients to capture the shock discontinuity in high-speed flows. In this paper, we demonstrate the performance of LAD when coupled with a high-order in-house solver COMPSQUARE, which uses central difference schemes (explicit and compact) for spatial discretization and an explicit fourth-order Runge–Kutta scheme for time integration. The efficacy of this method is tested on a variety of test cases which include a 1D stationary normal shock, 2D compression ramp, 2D incident oblique shock-boundary layer interaction, and a 3D compressible turbulent boundary layer. We further examine the efficacy of the scalar and directional forms of the artificial diffusivity method. On highly stretched grids with higher aspect ratios, the scalar formulation of LAD adds excessive artificial dissipation to the governing equations resulting in smaller time steps due to increased numerical stiffness. In contrast, the directional artificial diffusivity approach outperforms the scalar LAD on higher aspect ratio grids, as will be demonstrated for the test cases of the incident oblique shock and supersonic turbulent boundary layer. For the incident oblique shock test case in particular, the computation using directional LAD is 14.3 times faster than the scalar LAD.