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. (c) 2011 Elsevier Inc. All rights reserved.