A new LES model derived from generalized Navier-Stokes equations with nonlinear viscosity

TL;DR

This paper introduces a novel LES model derived from generalized Navier-Stokes equations with nonlinear viscosity, using the Clark approximation to close the subgrid-scale tensor, offering an alternative to traditional eddy viscosity models.

Contribution

It proposes a new LES modeling approach based on nonlinear viscosity in generalized Navier-Stokes equations, differing from classical models like Smagorinsky.

Findings

New LES model derived from generalized Navier-Stokes equations

Uses Clark approximation for subgrid-scale tensor closure

Offers an alternative to eddy viscosity-based models

Abstract

Large Eddy Simulation (LES) is a very useful tool when simulating turbulent flows if we are only interested in its "larger" scales. One of the possible ways to derive the LES equations is to apply a filter operator to the Navier-Stokes equations, obtaining a new equation governing the behavior of the filtered velocity. This approach introduces in the equations the so called subgrid-scale tensor, that must be expressed in terms of the filtered velocity to close the problem. One of the most popular models is that proposed by Smagorinsky, where the subgrid-scale tensor is modeled by introducing an eddy viscosity. In this work, we shall propose a new approximation to this problem by applying the filter, not to the Navier-Stokes equations, but to a generalized version of them with nonlinear viscosity. That is, we shall introduce a nonlinear viscosity, not as a procedure to close the subgrid-scale tensor, but as part of the model itself (see below). Consequently, we shall need a different method to close the subgrid-scale tensor, and we shall use the Clark approximation, where the Taylor expansion of the subgrid-scale tensor is computed.