中文摘要：

采用低马赫数近似的方法来对大温差驱动的自然对流问题进行数值模拟。低马赫数近似是通过将全可压的Navier—Stokes方程中声波进行过滤，从而在马赫数较低的流动中忽虑声波对流场的影响。声波过滤后的方程具有不可压缩N—S方程的特点，但可以求解温度和密度变化较大的问题。首先，通过对盖顶驱动流的数值模拟，验证了本文方法的可靠性。本文对常重力下，瑞利数为100的大温差驱动自然对流进行数值模拟，并且与简单不可压方程的结果进行比较，发现在大温差的情况下Boussineq假设并不能给出很精确的结果。

英文摘要：

The paper applied the Low Mach Number Method in the simulation of natural convection with large temperature gradient. Low Mach equations were obtained from fully compressible Navier-Stokes equations by filtering the pressure wave. So the influence of the pressure wave can be neglected and it can describe the variation of density with large temperature gradient, when the Mach number is very low. When Mach number approaches zero, this will be reduced to the incompressible Navier-Stokes equation. In this paper, the simulation of lid-cavity is firstly presented so that our procedure is verified. Then numerical simulation of natural convection with Ra=10^6 under the gravity was carried out, comparison with the results of incompressible equation with Boussineq approximation was obtained. We found the latter could not give accurate results when it comes to large temperature gradients.