发展了基于投影法的紧致方法求解流动换热问题，对顶盖驱动流和侧壁加热的方腔内自然对流换热问题进行了数值模拟。与其它传统方法相比，紧致方法能在较少的网格结点下获得精度较高的计算结果。进一步，采用所发展的紧致方法对不同工况下的Rayleigh—Benard对流及：其静态分岔现象进行了数值模拟。数值计算结果表明当长宽比变大时，底部努塞尔数会有小幅度增加。当长宽比为8时，用所发展的紧致方法不同的初场可以得出三种不同的流场和温度场。与基于QUICK格式的SIMPLE算法相比，所发展的紧致方法可以多预测一种静态分岔现象。
A compact finite difference scheme in the context of projection method is developed for flow and heat transfer. This scheme is applied for simulating driven cavity flow and natural convection in a square cavity with differentially heated side walls. Compared with classical finite difference method, compact finite difference method can get higher order accuracy on fewer grids. At the same time, this method is applied for solving Rayleigh-Benard flow at different cases and static bifurcation. The results indicate that the Nu numbers from below increase when the aspect ratio is changed. With an aspect ratio of 8, three different streamlines and temperature fields can be achieved at different initial conditions. Compared with SIMPLE algorithm with Quick scheme, compact finite difference method can predict one more static bifurcation phenomenon.
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