The filtering analog of the variational multiscale method in large-eddy simulation

The variational multiscale method introduced by Hughes et al. [Comput. Visual. Sci. 3, 47 (2000)] is extended to the classic filtering approach in large-eddy simulation. The role of the Germano identity in the formulation is precisely indicated. Multiscale methods based on standard eddy-viscosity models are related to (anisotropic) hyperviscosity models under certain conditions. Several models are tested and found to be as accurate as the standard dynamic model, while the implementations are more simple. Finally, the turbulent stress tensor is reformulated, such that filter and derivative in the filtered equations can be treated as a single operator.