dc.contributor.advisor |
Nassif, Nabil |
dc.contributor.advisor |
Moufawad, Sophie |
dc.contributor.author |
Saleh, Adel |
dc.date.accessioned |
2022-02-08T06:10:08Z |
dc.date.available |
2022-02-08T06:10:08Z |
dc.date.issued |
2/8/2022 |
dc.date.submitted |
2/7/2022 |
dc.identifier.uri |
http://hdl.handle.net/10938/23346 |
dc.description.abstract |
In Magnetohydrodynamics, the Hasegawa-Mima equation appears as a model for pseudo three-dimensional turbulence of a confined plasma inside a Tokamak reactor. This equation bears close resemblence to the 2d Navier-Stokes equation for an incompressible fluid. In this thesis, we apply an in time Euler implicit - space Finite Element Galerkin method to obtain solutions of this equation that satisfy periodic boundary values over the square. The Galerkin method readily provides us with a numerical scheme for which we prove convergence with minimal constraints on the time step, while making use of periodicity to obtain a priori esimates. Finally, we seek initial data for which the corresponding solution of the Hasegawa-Mima equation is a traveling wave. Those initial data turn out to be solutions to a semi-linear-elliptic periodic problem over a square, and we approximate them using a Newton-Galerkin method. |
dc.language.iso |
en |
dc.subject |
Periodic Sobolev Spaces |
dc.subject |
Finite Element Method |
dc.subject |
Fully Implicit Scheme |
dc.subject |
Galerkin Analysis |
dc.title |
Analysis and Implementation for an Time Euler Implicit - Space Finite ElementApproximation To a Hasegawa-Mima Plasma Model |
dc.type |
Thesis |
dc.contributor.department |
Department of Mathematics |
dc.contributor.faculty |
Faculty of Arts and Sciences |
dc.contributor.institution |
American University of Beirut |
dc.contributor.commembers |
Shayya, Bassam |
dc.contributor.commembers |
Antar, Ghassan |
dc.contributor.degree |
MS |
dc.contributor.AUBidnumber |
201101495 |