Abstract
In the current work, we develop a numerical method suitable for treating the problem of nonlinear two-dimensional flows in rectangular domains. For the spatial approximation we employ the Fourier-Galerkin approach. More specifically, our basis functions are products of trigonometric and Beam functions. This choice means that the solutions automatically satisfy the boundary and periodic conditions in the x and y directions respectively. The accuracy of the method is assessed by applying it to model problems which admit exact analytical solutions. The numerical and analytic solutions are found to be in good agreement. The convergence rate of the spectral coefficients is found to be fifth-order algebraic in the x-direction and y-direction, confirming the efficiency and speed of our technique.
Original language | English |
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Title of host publication | Application of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11 |
Pages | 97-105 |
Number of pages | 9 |
Volume | 1404 |
DOIs | |
Publication status | Published - 2011 |
Event | 3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11 - Albena, Bulgaria Duration: 20 Jun 2011 → 25 Jun 2011 |
Other
Other | 3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11 |
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Country/Territory | Bulgaria |
City | Albena |
Period | 20/06/11 → 25/06/11 |
Keywords
- beam functions
- nonlinear convective flow
- Spectral methods