|SUBJECT:||M.S. Thesis Presentation|
|TIME:||Thursday, March 31, 2011, 9:00 a.m.|
|TITLE:||A Numerical Investigation of Solving the Generalized Diffusion Equation Using Standard Diffusion Theory Methods in the Edge Pedestal|
|COMMITTEE:||Dr. W. M. Stacey, Chair (NRE)
Dr. Nolan Hertel (NRE)
Dr. Bojan Petrovic (NRE)
The presence of a large pinch velocity in the edge pedestal of high confinement (H-mode) tokamak plasmas implies that particle transport in the plasma edge must be treated by a pinch-diffusion theory, rather than a pure diffusion theory. Momentum balance also requires the inclusion of a pinch term in descriptions of edge particle transport. A numerical investigation of solving generalized pinch-diffusion theory using methods extended from the numerical solution methodology of pure diffusion theory hasbeen carried out. The generalized diffusion equation has been numerically integrated using the central finite-difference approximation for the diffusion term and three finite difference approximations of the pinch term, and then solved using Gauss reduction. The pinch-diffusion equation was solved directly and used as a benchmark for the finite-difference algorithm solutions to the generalized diffusion equation. Both equations are solved using different mesh spacings, and it is found that a finer mesh spacing will be required in the edge pedestal, where the inward pinch velocity is large in H-mode plasmas, than is necessary for similar accuracy further inward where the pinch velocity diminishes. An expression for the numerical error in various finite-differencing algorithms is presented.