Numerical scheme in polar coordinates for the analysis of convection in porous media

Authors

UDC

532.546:519.6

DOI:

https://doi.org/10.31429/vestnik-20-4-37-44

Abstract

The work is devoted to the numerical investigation of the convection of an incompressible heat-conducting fluid in a circle domain filled by porous media and heated from below. Based on the Darcy model using staggered grids, a numerical finite-difference scheme for solving equations in polar coordinates is developed. Discretization with a five-point stencil is used to provide a second order of accuracy. We propose special approximations in the pole's vicinity of a circular domain for the problem regarding the stream function and temperature. It is shown that the developed scheme preserves the cosymmetry of the problem. It is extremely important for further computation of the family of stationary regimes. We calculated the critical Rayleigh numbers for the problem with linear in vertical direction distribution of the temperature. The smallest one corresponds to the occurrence of convection.

Keywords:

convection in porous media, cosymmetry, critical values of the Rayleigh numbers, finite-difference scheme, circular enclosure

Acknowledgement

The work was supported by a grant from the Government of the Russian Federation (agreement No. 075-15-2019-1928).

Author Infos

Pavel V. Kokhanov

ассистент кафедры общей физики Физического факультета Южного федерального университета

e-mail: kohanov@sfedu.ru

Vyacheslav G. Tsybulin

д-р физ.-мат. наук, доцент кафедры Теоретической и компьютерной гидроаэродинамики Института математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета

e-mail: vgcibulin@sfedu.ru

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Issue

2023. Vol. 20. No. 4

Section

Mechanics

Pages

37-44

Submitted

2023-11-14

Published

2023-12-31

How to Cite

Kokhanov P.V., Tsybulin V.G. Numerical scheme in polar coordinates for the analysis of convection in porous media. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 4, pp. 37-44. DOI: https://doi.org/10.31429/vestnik-20-4-37-44 (In Russian)

Copyright (c) 2024 Kokhanov P.V., Tsybulin V.G.

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