Numerical study of the Boussinesq model of natural convection in an annular space: having a horizontal axis bounded by circular and elliptical isothermal cylinders

Abstract

The authors present a new calculation code using a two-dimensional finite element method valid in a steady and laminar flow. If the enclosure impedes the movement of the fluid, it becomes possible to observe multicellular flows even if the Rayleigh number is small. In this case, the increase of this number induces a fusion of the cells. If the Rayleigh number is large enough, there exists an interval of values of Rayleigh number for which the relaxation coefficients do not only influence the speed of calculation convergence but also the solution of transfer equation. Beyond this interval, the relaxation coefficients no longer influence this solution. At large values of Rayleigh number just before the divergence of the calculations, the stream function takes two values according to the value of relaxation coefficients, in case that the iterations number increases; this phenomenon is most manifest when the boundary conditions contain elements of symmetry in consideration of the vertical direction.