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The Navier-Stokes Voight Model and Convergence to equilibrium and statistical equilibrium

Koseoglu, Ali (2011) The Navier-Stokes Voight Model and Convergence to equilibrium and statistical equilibrium. Master's Thesis, University of Pittsburgh.

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    Abstract

    This thesis tests accelerating convergence to steady state and statistical equilibrium forthe Navier-Stokes Voight (NSV) Model motivated by the Spin-Up phase of Ocean ClimateModels. First, by adding a new parameter to Navier-Stokes equations, the NSV model isdetermined. Test conditions are identi…ed for spin up, attaining equilibrium, and statisticalequilibrium. Convergence is then analyzed and the Finite Element Method with BackwardEuler discretization is programmed using Free FEM++ to simulate the NSV model. Twoproblems with a known exact solution are used for a square domain. One problem withunknown solution and one problem with known exact solution in circle domain are alsotested for convergence of the method. We …nd that the adding parameter may not accelerateconvergence to equilibrium or statistical equilibrium.

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    Details

    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmail
    Committee ChairManfredi, Juan J.manfredi@pitt.edu
    Committee MemberGartside , Paulgartside@math.pitt.edu
    Committee MemberLayton, William J.wjl@pitt.edu
    Title: The Navier-Stokes Voight Model and Convergence to equilibrium and statistical equilibrium
    Status: Unpublished
    Abstract: This thesis tests accelerating convergence to steady state and statistical equilibrium forthe Navier-Stokes Voight (NSV) Model motivated by the Spin-Up phase of Ocean ClimateModels. First, by adding a new parameter to Navier-Stokes equations, the NSV model isdetermined. Test conditions are identi…ed for spin up, attaining equilibrium, and statisticalequilibrium. Convergence is then analyzed and the Finite Element Method with BackwardEuler discretization is programmed using Free FEM++ to simulate the NSV model. Twoproblems with a known exact solution are used for a square domain. One problem withunknown solution and one problem with known exact solution in circle domain are alsotested for convergence of the method. We …nd that the adding parameter may not accelerateconvergence to equilibrium or statistical equilibrium.
    Date: 14 September 2011
    Date Type: Completion
    Defense Date: 22 July 2011
    Approval Date: 14 September 2011
    Submission Date: 21 July 2011
    Access Restriction: No restriction; Release the ETD for access worldwide immediately.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Master's Thesis
    Refereed: Yes
    Degree: MS - Master of Science
    URN: etd-07212011-205723
    Uncontrolled Keywords: Navier Stokes Voight Model; Equilibrium; Spin up
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:52
    Last Modified: 17 Feb 2012 16:17
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-07212011-205723/, etd-07212011-205723

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