A connection between filter stabilization and eddy viscosity models

TL;DR

This paper establishes a theoretical link between a nonlinear filtering-based stabilization method for Navier-Stokes equations and eddy-viscosity models in LES, providing new insights into filter properties and convergence analysis.

Contribution

It demonstrates the equivalence of a nonlinear filtering stabilization approach to eddy-viscosity models, enabling refined analysis and understanding of filter characteristics.

Findings

Proves the equivalence between filter stabilization and eddy-viscosity models.

Provides convergence estimates for filtered numerical solutions to DNS.

Analyzes the application of filtering within a projection method for Navier-Stokes equations.

Abstract

Recently, a new approach for the stabilization of the incompressible Navier-Stokes equations for higher Reynolds numbers was introduced based on the nonlinear differential filtering of solutions on every time step of a discrete scheme. In this paper, the stabilization is shown to be equivalent to a certain eddy-viscosity model in LES. This allows a refined analysis and further understanding of desired filter properties. We also consider the application of the filtering in a projection (pressure correction) method, the standard splitting algorithm for time integration of the incompressible fluid equations. The paper proves an estimate on the convergence of the filtered numerical solution to the corresponding DNS solution.