A High-Accurate Fourier-Galerkin Solution for Buoyancy-Driven Flow in a Square Cavity

Abstract

In this work, a high-accurate solution is proposed for the verification of coupled fluid flow and heat transfer codes. The solution, based on the Fourier-Galerkin (FG) method, is developed for free convection in a square cavity with Rayleigh numbers ranging from 10³ to 10⁸. The Fourier coefficients are calculated by solving a highly nonlinear system of algebraic equations using Powell's method. The FG results are then used as reference solutions to study the performance of a finite-element model and to illustrate the benefit of the developed solutions in benchmarking buoyancy-driven flows.

Notes

*Did not converge.

*Did not converge.