A study of natural convection in three dimensional square plates is investigated numerically. Several open boundaries co-exist in the physical domain, and a non-reflecting boundary condition applied at the aperture is no longer suitable for solving the problem of this study. An absorbing boundary condition is then adopted and modified in the solution processes. Methods of the Roe scheme, preconditioning and dual time stepping matching LSUGS scheme are used to solve a situation of a low speed compressible flow. The geometry of the physical model is the parallel square plates, and the parameter of Rayleigh number is not high, and then phenomena observed are almost symmetrical. The results of the work have good agreements with the experimental results of a previous paper. (c) 2012 Elsevier Ltd. All rights reserved.