A mathematical and numerical study of a filtering-based multiscale fluid model with nonlinear eddy viscosity

This report investigates a Smagorinsky type eddy viscosity model recently proposed by Vreman (2003) in  [4]. The model employs a filter operation to represent the small resolved scales and, similar to variational multiscale methods, uses only these small resolved scales to describe the effect of the unresolved scales on the resolved ones. We prove well-posedness of the model, and formulate, analyze and test finite element algorithms for it.