Inverse formulation and finite difference solution for flow from a circular orifice
Inverse formulation and finite difference solution for flow from a circular orifice
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圆形孔口流量的反演公式和有限差分解
DOI：
10.1017/s0022112070000137
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发表时间：
1970
影响因子：
3.7
通讯作者：
R. Jeppson
中科院分区：
文献类型：
--
作者：
R. Jeppson
本文以速度势和Stokes流函数为自变量，以径向和轴向尺寸为因变量，建立了大型水库通过圆孔的流动问题的方程，并对所得边值问题求得了有限差分解。这种逆公式的优点是在物理平面上的有限差分解，即流动区域是矩形的，因此很好地适用于数字计算机编程中的最小逻辑。尽管逆偏微分方程和相关的边界条件是非线性的，但逆有限差分解比物理平面上的可比解更容易获得。从逆有限差分解的结果是在密切的协议与其他最近的结果从近似解这个问题。这种反解方法也适用于其它自由流线及有约束轴对称势流问题。其他问题的本质区别在于边界条件。关键词：孔板，有限差分，非线性偏微分方程，势流。
The problem of flow from a large reservoir through a circular orifice is formulated by considering the velocity potential and Stokes's stream function as the independent variables and the radial and axial dimensions as the dependent variables, and a finite difference solution is obtained to the resulting boundary-value problem. This inverse formulation has the advantage over a finite difference solution in the physical plane that the region of flow is rectangular and consequently well adapted for minimum logic in programming a digital computer. The inverse finite difference solution is more readily obtained than a comparable solution in the physical plane, even though the inverse partial differential equation and associated boundary conditions are non-linear. The results from the inverse finite difference solution are in close agreement with other most recent results from approximate solutions to this problem. The inverse method of solution is applicable to other free streamline as well as confined axisymmetric potential flow problems. The essential difference in other problems will be in the boundary conditions.Keywords: Orifice, Finite Differences, Non-linear Partial Differential Equation, Potential Flow.