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Numerical analysis of modular regularization methods for theBDF2 time discretization of the Navier-Stokes equations∗

Published online by Cambridge University Press:  01 April 2014

William Layton ,
Nathaniel Mays ,
Monika Neda  and
Catalin Trenchea
William Layton
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA. . wjl@pitt.edu
Nathaniel Mays
Affiliation:
Department of Mathematics, Wheeling Jesuit University, Wheeling, WV, 26003, USA.; nmays@wju.edu
Monika Neda
Affiliation:
Department of Mathematical Sciences, University of Nevada Las Vegas, USA.; Monika.Neda@unlv.edu
Catalin Trenchea
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA. ; trenchea@pitt.edu
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Abstract

We consider an uncoupled, modular regularization algorithm for approximation of theNavier-Stokes equations. The method is: Step 1.1: Advance the NSEone time step, Step 1.1: Regularize to obtain the approximation atthe new time level. Previous analysis of this approach has been for specific time steppingmethods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled,modular stabilization to (i) the more complex and better performing BDF2 timediscretization in Step 1.1, and (ii) more general (linear ornonlinear) regularization operators in Step 1.1. We give a completestability analysis, derive conditions on the Step 1.1regularization operator for which the combination has good stabilization effects,characterize the numerical dissipation induced by Step 1.1, provean asymptotic error estimate incorporating the numerical error of the method used in Step1.1 and the regularizations consistency error in Step 1.1 and provide numerical tests.

Keywords

Modular regularizationBDF2 time discretizationNavier-Stokes equationsturbulencefinite element method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 3 , May 2014 , pp. 765 - 793
Copyright
© EDP Sciences, SMAI 2014

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