A connection between filter stabilization and eddy viscosity models. Issue 6 (18th May 2013)

• Record Type: Journal Article
• Authors: Olshanskii, Maxim A.; Xiong, Xin
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 6(2013:Nov.)
• Page Start: 2061
• Page End: 2080
• Publication Date: 2013-05-18
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21791
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>Recently, a new approach for the stabilization of the incompressible Navier–Stokes equations for high Reynolds numbers was introduced based on the nonlinear differential filtering of solutions on every time step of a discrete scheme. In this article, the stabilization is shown to be equivalent to a certain eddy‐viscosity model in Large Eddy Simulation. 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 article proves an estimate on the convergence of the filtered numerical solution to the corresponding Navier‐Stokes solution. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013</p> </abstract>