A study of LIE group method and its application to solve the unsteady transonic flow

The non-linear equations of motion describing the unsteady transonic flow in cartesian coordinates are considered in this dissertation. A method known as Lie group which reduce the non-linear partial differential equation to an ordinary differential equation on the basis of the underlying symmetry...

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Main Author: Mohammad Huskhazrin, Kharuddin
Format: Thesis
Language:English
Subjects:
Online Access:http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/42991/1/P.1-24.pdf
http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/42991/2/Full%20Text.pdf
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Summary:The non-linear equations of motion describing the unsteady transonic flow in cartesian coordinates are considered in this dissertation. A method known as Lie group which reduce the non-linear partial differential equation to an ordinary differential equation on the basis of the underlying symmetry structure has been used. The Lie method is quite useful in reducing a complex equation to an easy-to-handle ordinary differential equation. By employing the Lie theory, the full one-parameter infinitesimal transformation group leaving the equations of motion invariance is derived along with its associated Lie algebra. Subgroups of the full group are then used to obtain a reduction by one in the number of independent variables in the system. These reductions are continued until an ordinary differential equation is reached. A series type exact solution of these reduced ordinary differential equation is obtained which leads to a series type exact solution of the unsteady transonic flow equation. The Lie group method seems to be an appropriate choice to handle these nonlinear equation.