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Title:Applications of Lie Group Methods to the Equations of Magnetohydrodynamics
Author(s):Mandrekas, John
Department / Program:Nuclear Engineering
Discipline:Nuclear Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Physics, Fluid and Plasma
Abstract: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.
Issue Date:1987
Description:214 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987.
Other Identifier(s):(UMI)AAI8721704
Date Available in IDEALS:2014-12-16
Date Deposited:1987

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