非定常流函数涡量方程的一种数值解法的研究

STUDY OF ONE NUMERICAL METHOD FOR SOLVING THE UNSTEADY EQUATIONS OF STREAM AND VORTICITY FUNCTIONS

摘要: 对非定常流函数涡量方程的数值求解方法进行了改进，其中流函数一阶导数即速度项采用四阶精度的Hermitian公式，对流项由一般二阶精度的中心差分提高到四阶精度离散差分，包含温度方程在内的离散方程组采用ADI迭代方法求得定常解．以无内热体及有一内热体的封闭方腔内自然对流为例，进行了不同瑞利数（Ra）条件下的数值研究．结果表明，该方法推导简单，求解精度高且计算稳定，适用于封闭腔内高瑞利数复杂混合对流的数值模拟．

Abstract: The method for solving the unsteady equations of stream and vorticity functions has been improved. The Hermitian formulas of forth-order accuracy are adopted for first partial derivatives of stream function (i.e. velocities). The forth-order accuracy finite difference is used for the convective terms instead of the second-order central difference. The ADI successive method is used for solving the equations which contain the temperature equation to obtain the steady solutions.Second-order central difference ...