Abstract
We present the adaptation to non-free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck-Boussinesq equations in a Rayleigh-Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number ($$R\sim10^9$$). These results are the basis for the later study, by the same method, of wet convection in a solar still.Received: 20 Novembre 2014, Accepted: 15 September 2015; Edited by: C. A. Condat, G. J. Sibona; DOI:http://dx.doi.org/10.4279/PIP.070015Cite as: I C Ramos, C B Briozzo, Papers in Physics 7, 070015 (2015)This paper, by I C Ramos, C B Briozzo, is licensed under the Creative Commons Attribution License 3.0.
Highlights
Experimental observations [1] show that the onset of a turbulent convective flux can significantly enhance the efficiency of a basin-type solar still, but until now a theoretical explanation is lacking
We present the adaptation to non–free boundary conditions of a pseudospectral method based on the Fourier transform
The method is applied to the numerical integration of the Oberbeck–Boussinesq equations in a Rayleigh–Benard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature
Summary
Experimental observations [1] show that the onset of a turbulent convective flux can significantly enhance the efficiency of a basin-type solar still, but until now a theoretical explanation is lacking. Dospectral methods are the simplest and fastest, since the discretized spatial differential operators are local, nonlinear terms can be computed through Fast Fourier Transform (FFT) convolutions, and solving the Poisson equation originating from the incompressibility (divergence-free) condition is almost trivial. They usually work only for free (periodic) boundary conditions (BCs). We will show how a Fourier-based pseudospectral method can be adapted to simple non-free (but periodic) BCs without losing its more appealing features This is a first step towards building a pseudospectral simulation of wet air convection inside a basin-type solar still, and must be considered just as a proof of concept.
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