High-Order Finite-Difference Schemes for (Hyper-) Viscous Filtering on Non-Uniform Meshes

In this study, the viscous filtering technique is extended to one-sided and biased finite-difference schemes for non-uniform meshes. The most attractive feature of this technique lies in its numerical stability despite the use of a purely explicit time advancement. This feature is well recovered for non-uniform meshes, making the approach as a simple and efficient alternative to the implicit time integration of the viscous term in the context of direct and large-eddy simulation. The rationale to develop generalized filter schemes is presented. After a validation based on the Burgers solution while using a refined mesh in the shock region, it is shown that a high-order formulation can be used to ensure both molecular and artificial dissipation for performing implicit LES of transitional boundary layer while relaxing drastically the time step constraint.