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:	Transonic flow Non-linear equations Lie group Infinitesimal transformation Finite transformation group Invariance
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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spelling	my-unimap-429912016-09-22T07:53:58Z A study of LIE group method and its application to solve the unsteady transonic flow Mohammad Huskhazrin, Kharuddin Dr. Kamran Fakhar 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. Universiti Malaysia Perlis (UniMAP) 2014 Thesis en http://dspace.unimap.edu.my:80/xmlui/handle/123456789/42991 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/42991/3/license.txt 8a4605be74aa9ea9d79846c1fba20a33 http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/42991/1/P.1-24.pdf 22c77c0142fe811ff49c06826b36ccdd http://dspace.unimap.edu.my:80/xmlui/bitstream/123456789/42991/2/Full%20Text.pdf 44e4642e92e01aa35c56f5469a70d5fc Transonic flow Non-linear equations Lie group Infinitesimal transformation Finite transformation group Invariance Institute of Engineering Mathematics
institution	Universiti Malaysia Perlis
collection	UniMAP Institutional Repository
language	English
advisor	Dr. Kamran Fakhar
topic	Transonic flow Non-linear equations Lie group Infinitesimal transformation Finite transformation group Invariance
spellingShingle	Transonic flow Non-linear equations Lie group Infinitesimal transformation Finite transformation group Invariance Mohammad Huskhazrin, Kharuddin A study of LIE group method and its application to solve the unsteady transonic flow
description	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.
format	Thesis
author	Mohammad Huskhazrin, Kharuddin
author_facet	Mohammad Huskhazrin, Kharuddin
author_sort	Mohammad Huskhazrin, Kharuddin
title	A study of LIE group method and its application to solve the unsteady transonic flow
title_short	A study of LIE group method and its application to solve the unsteady transonic flow
title_full	A study of LIE group method and its application to solve the unsteady transonic flow
title_fullStr	A study of LIE group method and its application to solve the unsteady transonic flow
title_full_unstemmed	A study of LIE group method and its application to solve the unsteady transonic flow
title_sort	study of lie group method and its application to solve the unsteady transonic flow
granting_institution	Universiti Malaysia Perlis (UniMAP)
granting_department	Institute of Engineering Mathematics
url	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
_version_	1747836820489502720

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

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