Date of Award
5-2010
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Legacy Department
Mathematical Science
Committee Chair/Advisor
Rebholtz, Leo
Committee Member
Cox , Chris
Committee Member
Kaye , Nigel
Abstract
This thesis is an investigation of numerical methods for approximating solutions to fluid flow problems, specifically the Navier-Stokes equations (NSE) and magnetohydrodynamic equations (MHD), with an overriding theme of enforcing more physical behavior in discrete solutions. It is well documented that numerical methods with more physical accuracy exhibit better long-time behavior than comparable methods that enforce less physics in their solutions. This work develops, analyzes and tests finite element methods that better enforce mass conservation in discrete velocity solutions to the NSE and MHD, helicity conservation for NSE, cross-helicity conservation in MHD, and magnetic field incompressibility in MHD.
Recommended Citation
Case, Michael, "Improved Accuracy for Fluid Flow Problems Via Enhanced Physics" (2010). All Dissertations. 561.
https://tigerprints.clemson.edu/all_dissertations/561