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Modelling of Marangoni convection using proper orthogonal decomposition

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Abstract

Proper orthogonal decomposition (POD) is applied to Marangoni convection in a horizontal fluid layer heated from below and cooled from above with non-deformable free surface. We investigate two-dimensional Marangoni convection for the case of free-slip bottom in the limit of small Prandtl number. The POD technique is then used to the velocity and temperature data to obtain basis functions for both velocity and temperature fields. When these basis functions are used in a Galerkin procedure, the low-dimensional of Marangoni convection are constructed with the smallest possible degree of freedom. The results based on this low-dimensional model are discussed.

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Authors and Affiliations

  1. Department of Mathematics, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

    N. M. Arifin & A. Kiliçman

  2. School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia

    M. S. M. Noorani

Authors
  1. N. M. Arifin
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  2. M. S. M. Noorani
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  3. A. Kiliçman
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Correspondence to N. M. Arifin.

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Arifin, N.M., Noorani, M.S.M. & Kiliçman, A. Modelling of Marangoni convection using proper orthogonal decomposition. Nonlinear Dyn 48, 331–337 (2007). https://doi.org/10.1007/s11071-006-9052-x

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  • DOI: https://doi.org/10.1007/s11071-006-9052-x

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