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Some experiments with adaptive penalty methods in the numerical solution of the incompressible Navier-Stokes equations

Berge, Astrid (2021) Some experiments with adaptive penalty methods in the numerical solution of the incompressible Navier-Stokes equations. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

This paper presents and tests an adaptive scheme for the penalty method. First, the penalty method is introduced as an optimization method and then applied to the Navier-Stokes equations. The energy equation, proof of stability and consistency error of the penalty method is given. Some computational tests of the penalty method in FEniCS are presented, showing the first-order convergence, with plots of the error. A sample code to recreate the results is included. Next, the idea of an adaptive method is discussed and presented in the case of the penalty method, adapted from a recent paper.
The energy equation and inequality are given, showing stability. Numerical experiments in FEniCS are presented for a fixed timestep and varying epsilon, as well as a test of the doubly adaptive scheme.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Berge, Astridastridi@me.comaib27
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, Williamwjl@pitt.edu
Committee MemberNeilan, Michaelneilan@pitt.edu
Committee MemberTrenchea, Catalintrenchea@pitt.edu
Date: 20 January 2021
Date Type: Publication
Defense Date: 30 November 2020
Approval Date: 20 January 2021
Submission Date: 2 December 2020
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 50
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: Navier-Stokes, penalty method, timestepping
Date Deposited: 20 Jan 2021 19:28
Last Modified: 20 Jan 2021 19:28
URI: http://d-scholarship.pitt.edu/id/eprint/40104

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