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Mandrekas, John 2014-12-16T04:17:41Z 2014-12-16T04:17:41Z 10000-01-01 1987 1987 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. Made available in DSpace on 2014-12-16T04:17:41Z (GMT). No. of bitstreams: 1 8721704.pdf: 4954832 bytes, checksum: 145e957c4a3834fdbf11a7498a2081c2 (MD5) Previous issue date: 1987 Embargo set by: Seth Robbins for item 71075 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 214 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987. http://hdl.handle.net/2142/70909 (UMI)AAI8721704 Physics, Fluid and Plasma Applications of Lie Group Methods to the Equations of Magnetohydrodynamics text Nuclear Engineering Nuclear Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.