A beam-fourier technique for the numerical investigation of 2D nonlinear convective flows

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationApplication of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11
Pages97-105
Number of pages9
Volume1404
DOIs
Publication statusPublished - 2011
Event3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11 - Albena, Bulgaria
Duration: 20 Jun 201125 Jun 2011

Other

Other3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11
CountryBulgaria
CityAlbena
Period20/06/1125/06/11

Keywords

  • beam functions
  • nonlinear convective flow
  • Spectral methods

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    Papanicolaou, N. C. (2011). A beam-fourier technique for the numerical investigation of 2D nonlinear convective flows. In Application of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11 (Vol. 1404, pp. 97-105) https://doi.org/10.1063/1.3659908