Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation

In this short note, we show how to use a highly accurate finite-difference scheme to compute second derivatives in the Navier–Stokes equations while ensuring targeted numerical dissipation. This approach, essentially non conservative, is shown to be close to an upwind method and is straightforward to implement with a negligible computational extra cost. The benefit offered by the resulting discrete operator is illustrated for the direct computation of sound in aeroacoustics and in the more general context of large-eddy simulation through connections with hyperviscosity and spectral vanishing viscosity.