Residual-Based Variational MultiScale LES for the Finite Volume Method

The finite volume method has been previously combined with the Streamline-upwind Petrov Galerkin (SUPG) method, originally developed for finite elements. The purpose of SUPG is to stabilize the numerical method for advection-dominated flows. The control volume formulation augmented with SUPG has been coined the streamline upwind control volume (SUCV) method by its original developers and has been shown to lead to convergent results for heat transfer problems. Here we review the SUCV and cast it within the context of residual-based variational multiscale (RBVMS) modeling for large-eddy simulation (LES). The subgrid-scale (SGS) model that results is expressed in terms of a SGS anisotropic viscosity and stress. The new RBVMS LES formulation on a finite volume discretization will be shown to provide improved results relative to traditional LES with the dynamic Smagorinsky model on the same discretization in terms of mean velocity and root mean square of velocity for turbulent channel flows at various friction Reynolds numbers.