Applications of Lie Group Methods to the Equations of Magnetohydrodynamics

The invariance properties of various sets of magnetohydrodynamic (MHD) equations are studied using techniques from the theory of differential forms. Equations considered include the ideal MHD equations in different geometries and with different magnetic field configurations, the MHD equations in the presence of gravitational forces due to self-attraction or external fields, and the MHD equations including finite thermal conductivity and magnetic viscosity. The knowledge of the group structure of these equations is then used to introduce similarity variables to these equations. For each choice of similarity variables, the original set of partial differential equations is transformed into a set of ordinary differential equations and the most general form of the initial conditions is determined. Three cases are studied in detail and the corresponding sets of ordinary differential equations are solved numerically: The problem of a blast wave in an inhomogeneous atmosphere, the problem of a piston moving according to a power law in time, and the problem of a piston moving according to an exponential law in time.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Nuclear Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Mandrekas, John

• Physics, Fluid and Plasma

Identifier

(UMI)AAI8721704

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/70909