A Petrov-Galerkin method for flows in cavities: enclosure of aspect ratio 8

Abstract

A Petrov-Galerkin method for computations of fully enclosed flows is developed. It makes use of divergence-free basis functions which also satisfy the boundary conditions for the velocity field. This allows the elimination of the unknown pressure. The computational procedure reduces to the solution of a system of nonlinear first order ordinary differential equations for the spectral expansion coefficients. We illustrate the effectiveness and accuracy of the method by solving the problem of the two-dimensional thermoconvective flow in a rectangular cavity of aspect ratio 8 at Rayleigh number 3.4 x 10^5.