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 | ||||||||||||
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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Status: | Unpublished | ||||||||||||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; The work is available 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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