Short Note: Hyperviscosity for shock-turbulence interactions

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Numerical Methods for High-Speed Flows (2011, background): “Cook & Cabot (2004, 2005) carried over the idea of selectively damping the highest resolved wavenumbers to physical space, through addition of an artificial stress tensor σ∗ij = 2µ ∗ Sij + (β ∗ − 2/3µ∗)uk,k δij , (33) where Sij = 1/2 (ui,j + uj,i).”
Breakdown mechanisms and heat transfer overshoot in hypersonic zero pressure gradient boundary layers (2013, methodology): “A common approach for high-order methods based on compact finite differences is the addition of artificial viscosity and thermal conductivity only in regions containing shocks (Cook & Cabot 2004, 2005).”
Artificial Fluid Properties for Large-Eddy Simulation of Compressible Turbulent Mixing (2007, methodology): “This work extends previous work on hyperviscosity [Cook and Cabot, 2004, 2005, Fiorina and Lele, in press] to include 3 hyperconductivity for contact discontinuities and hyperdiffusivity for material interfaces.”