控制容积平衡法在一维、稳态且含内热源导热微分方程中的应用

The Application of Control-volume Method to the Numerical Solution of the One-dimensional Stable Heat Conduction Differential Equation Containing Internal Heat Source

首先采用区域离散方法 A和区域离散方法 B分别划分计算网格节点,然后采用控制容积平衡法对某一维、稳态且含内热源导热微分方程进行了数值求解,并与其解析解(精确解)进行了比较。计算结果表明:控制容积平衡法物理意义明确,数值求解精度高,且随网格划分节点数的增加计算精度进一步提高;对于这两种网格划分方法,其网格节点处的离散方程推导均简单明了,且都具有统一的形式,因此对计算节点数增加的情况具有很大的适应性,有利于计算机编程实现。

To solve the one-dimensional stable heat-conduction differential equation containing internal heat source,first two zone griddivision method （Practice A and Practice B） were used to divide the grid nodes,then the control volume method was used to get theses nodes＇ temperature values numerically,and compared to these nodes＇ analytical values.The computation results show that the control volume method has a clear physical meaning and high accuracy of numerical solutions which still increases as the number of the grid nodes increase.For the two zone grid-division method,the deduction of each grid node＇ s difference equation is simple and similar which adapts the situation of increased grid nodes,so it＇s easy to generate the program codes to solve this type of differential equation numerically.