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Modelling of Marangoni convection using proper orthogonal decomposition. (English) Zbl 1180.76056

Summary: 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.

MSC:

76R10 Free convection
76D45 Capillarity (surface tension) for incompressible viscous fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
80A20 Heat and mass transfer, heat flow (MSC2010)
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