A Reference Benchmark Solution for Free Convection in A Square Cavity Filled with A Heterogeneous Porous Medium

Abstract

The Fourier-Galerkin (FG) method is used to produce a highly accurate solution for free convection in a square cavity filled with heterogeneous porous medium. To this end, the governing equations are reformulated in terms of the temperature and the stream function. These unknowns are then expanded in infinite Fourier series truncated at given orders. The accuracy of the FG solution is investigated for different truncation orders and compared to the results of an advanced finite-element numerical model using fine-mesh discretization. The obtained results represent a set of high-quality data that can be used for benchmarking numerical models.