MLPG method for the two-dimensional time dependent convection-diffusion equation
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Author list: Khankham S., Aschariyaphotha N., Luadsong A., Yomsatieankul W.
Publisher: Pushpa
Publication year: 2012
Journal: Far East Journal of Mathematical Sciences (0972-0871)
Volume number: 67
Issue number: 2
Start page: 229
End page: 247
Number of pages: 19
ISSN: 0972-0871
Languages: English-Great Britain (EN-GB)
Abstract
The meshless local Petrov-Galerkin (MLPG) upwinding scheme is presented for solving time dependent convection-diffusion equation in two-dimensional case. It is well known that convection-dominated flows are some of the most difficult problems to solve numerically. The presence of the convection term causes serious numerical difficulties, appearing in the form of oscillatory solutions, when the convection term is dominant. It can be shown in this paper that the MLPG upwinding scheme will be very promising to solve the convection-dominated flow problem. The numerical results of the time dependent convection-diffusion equation are investigated, and confirm that oscillations can be controlled by the MLPG upwinding scheme method. The convection-diffusion equation that solved by using time dependent equation has the better results than time independent equation. The results also show that the MLPG upwinding scheme gives stability results, while the MLPG without upwinding scheme gives unconditionally stable results. ฉ 2012 Pushpa Publishing House.
Keywords
Convection-diffusion equation, Time dependent, Upwinding scheme