Bassem Girgis

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering

Committee Chair

Sarma Rani

Committee Member

H. W. Coleman

Committee Member

Robert A. Frederick Jr.

Committee Member

Francis C. Wessling

Committee Member

Kader Frendi


Computational fluid dynamics., Plasma electrodynamics., Finite differences., Time-domain analysis.


The Flowfield Dependent Variation (FDV) method is a generalized numerical method for solving the partial differential equations that govern fluid dynamics, heat transfer, as well as multi-physics scenarios involving external electric and magnetic fields, and shock-turbulent boundary layer interactions. A unique feature of the FDV method is that most of the currently available Finite Difference Method (FDM) and Finite Element Method (FEM) computational schemes can be obtained from it as special cases. For this reason, the FDV method has the potential for application to a broad range of problems in science and engineering. The principal objective of this dissertation is to extend the FDV method to magnetohydrodynamic applications, specifically those applications that involve plasma dynamics. To achieve this objective, a parallel, arbitrarily high order, unstructured, implicit, 1D/2D/3D finite element method-based numerical framework has been developed and implemented. An Element-by-Element (EBE) data structure is used to store the linear system of equations, and the Generalized Minimal RESidual (GMRES) iterative solver is employed to solve the linear system. To ensure load balancing and achieve efficient parallel processing, domain decomposition is performed using the METIS software package. In addition, an EBE data structure-based distributed memory model is introduced that uses the Message Passing Interface (MPI) library. The efficiency of the parallel framework and the accuracy of the numerical method implementation were ensured through comprehensive verifications. Code verification involved a large number of benchmark problems in fluid dynamics and plasma dynamics that covered a broad spectrum of flow conditions. Results from the test cases considered showed good to excellent agreement with the data from the published literature. After completing the verification of the code, an in-depth study of the problems involving freely decaying isotropic and anisotropic turbulence was undertaken. The anisotropic turbulence problems involved exploring the effects of combining isotropic turbulence with an external, applied uniform magnetic field.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.