Sub-grid properties and artificial viscous stresses in staggered-mesh schemes

We show that, in the limit of smooth flows, Christensen's approach of applying limiters to the components of a low-order artificial viscosity is analytically equivalent to a high-order scheme. However, the directionally-split implementation suggested in the original publication leads to damping of low Mach number Kelvin-Helmholtz roll up problems similar to that previously observed for finite-volume Godunov schemes.