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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| Format: | Thesis |
| Language: | English |
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| 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. |
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