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• W1993454565 abstract "Any solenoidal vector field can be written in terms of two scalar fields. Solving the Navier-Stokes equation for these two so-called potentials is a widely used method, although difficulties have been reported in using this method to describe non-Cartesian confined flows, in particular cylindrical geometries. Difficulties arise because the potentials are coupled at the boundaries but also because of possible numerical instabilities associated with the high order of the equations. This paper shows how all these difficulties can be circumvented: firstly by properly deriving the required boundary conditions, but also through an adequate discretization, which is the final requirement. The use of spectral methods together with a reduction of order for the axisymmetric modes is sufficient for this purpose. In this paper, as a test, a velocity potentials method is used to solve the stability problem for the onset of convection in a fluid confined in a cylindrical container." @default.
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• W1993454565 date "1993-12-01" @default.
• W1993454565 modified "2023-09-27" @default.
• W1993454565 title "Thermal convection in vertical cylinders. A method based on potentials of velocity" @default.
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• W1993454565 doi "https://doi.org/10.1016/0045-7825(93)90026-t" @default.
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