剧变截面圆管内渗流的数值计算方法

A numerical computational method for the flow in porous media in the circular pipe with rapid-changed cross-section

对于剧变截面圆管的渗流问题写出不可压缩渗流的基本方程组,对直接求解原始变量(速度和压力)的数值计算方法作出改进。先由非主流方向的运动方程计算压力,后由主流方向的运动方程计算主流方向的速度分量,再由连续性方程计算非主流方向的速度分量。这样可以避免在一般的求解原始变量方法中由连续性方程计算压力时出现的困难和麻烦。根据本方法和剧变截面圆管的特点,采用半交错不等距非正交贴体混合网格系。本文详细写出差分方程和迭代计算公式,对剧变截面圆管内的渗流算例进行数值计算。本方法的优点是简单和实用,在工程上具有较大的应用价值。

The fundamental equations of the incompressible flow in porous media were written for the flow in porous media in the circular pipe with rapid-changed cross-section. The numerical computational method to solve original variables (velocity and pressure) was improved in the paper. Finality the motion equation on non-main-flow direction was used to compute the pressure. Then the motion equation on main-flow direction was used to compute the velocity component on main-flow direction. Finally the continuity equation was used to compute the velocity component on non-main-flow direction. The difficulty and trouble, which were introduced in general method to compute pressure from the continuity equation can be avoided. The semi-staggered, non-equidistante non-orthogonal mixed mesh system is used by base of the characteristics of the method and the circular pipe with rapid-changed cross-section. The difference equation and computational formula for iteration computation were written in detail. The examples of the flow in porous media in the circular pipe with rapid-changed cross-section were numerically computed. The advantages of the method are its simplicity and practicability. So the method has extensive application values in the engineering.