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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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 |