Viscous and hyperviscous filtering for direct and large-eddy simulation

Highlights: • A new solution filtering technique for direct and large-eddy simulation is proposed. • The novelty is that both the molecular and artificial dissipations are represented. • Only coefficients have to be coded in a conventional finite-difference routine. • This is an efficient alternative to implicit time integration of the viscous term. • Connections are established with spectral vanishing viscosity for implicit LES. This work is dedicated to the solution filtering technique for performing direct and large-eddy simulation. It is shown that this approach is equivalent to the use of spectral viscosity as a possible ersatz of subgrid-scale modelling. In the framework of finite-difference schemes, the filter operator can be designed to ensure time consistency while easily controlling the level and scale selectivity of the dissipation thus introduced. Then, a new family of filter schemes is developed in order to represent both the molecular and artificial dissipations. The resulting viscous filter operator is straightforward to implement through a simple modification of its coefficients that depend on the molecular/artificial viscosity and the time step. A definitive advantage in terms of computational efficiency is obtained for computational configurations where the time step is restricted by the Fourier condition, as a simple alternative to implicit time integration of the viscous term. Numerical tests clearly show that this viscous filtering method is flexible, accurate and numerically stable at large Fourier number.