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A connection between filter stabilization and eddy viscosity models

Authors

  • Maxim A. Olshanskii,

    Corresponding author
    1. Department of Mathematics, University of Houston, Houston, Texas 77204-3008
    2. Department of Mechanics and Mathematics, Moscow State University, Moscow 119899
    • Department of Mathematics, University of Houston, Houston, Texas 77204-3008
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  • Xin Xiong

    1. Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
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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

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