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A connection between filter stabilization and eddy viscosity models
Author(s) -
Olshanskii Maxim A.,
Xiong Xin
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21791
Subject(s) - mathematics , filter (signal processing) , nonlinear system , compressibility , convergence (economics) , reynolds number , navier–stokes equations , mathematical analysis , projection (relational algebra) , partial differential equation , turbulence modeling , connection (principal bundle) , viscosity , geometry , algorithm , computer science , mechanics , physics , turbulence , quantum mechanics , economics , computer vision , economic growth
Abstract 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