A parameter-free dynamic subgrid-scale model for large-eddy simulation

We present a new dynamic Smagorinsky subgrid-scale model in which the sole model parameter, the filter width ratio, is computed dynamically. The resulting expression for the filter width ratio is parameter-free, as difficult-to-compute filter widths required in earlier models are no longer necessary. Traditionally, the filter width ratio is taken as a constant based on assumptions which do not hold in general for all numerical discretizations. Previous work has shown that simulation results may strongly depend on the filter width ratio parameter, thus motivating its accurate determination. The new dynamic model is tested on large-eddy simulation of decaying isotropic turbulence on hexahedral, tetrahedral, and wedge topologies using the stabilized finite element method developed by Whiting and Jansen [C.H. Whiting, K.E. Jansen, A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis, Int. J. Numer. Methods Fluids 35 (2001) 93–116].