Solution of Velocity at Moving Interfaces between Fresh-and Salt-Water in Aquifers
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摘要: 提出了基于Shwarz-Christoffel变换求解含水层咸淡水移动界面流速的方法,其基本步骤为:(1)将流动平面z的淡水区和咸水区分别映射为辅助平面tf和ts的上半部分;(2)利用tf和ts平面与复势平面wf和ws的映射关系并引入某些几何参数,建立关于复势多边形边长比方程,则问题归结为这些参数的求解;(3)建立关于边界条件的方程,其中包括淡水入流条件和物质面条件;(4)联立求解这些方程并求解界面流速。这一方法与一般数值方法的区别主要是直接求解流速,不需要将流动区域离散化,因而误差较小。算例表明这种方法是可行的。
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关键词:
- 地下水 /
- 界面 /
- Schwarz－Christoffel变换
Abstract: A method based on the Schwarz-Christoffcl trans-formation is developed for the solution of velocity at moving interfaces between fresh-and salt-water in aquifers. It involves the following primary steps:(1)Map the given fresh-and salt-water regions of the flow plane Z onto the upper halves of auxiliary planes tf and ts, respectively. (2) Use a mapping between the planestfandl,and the complex potential planes wf and ws to set up equations for the side-length rations of complex potential polygons,containing some geometric parameters,so that the problem becomes one of solution for the parameters. (3) Set up equations for boundary conditions, including those of fresh-water influx and material interface. (4) Solve the coupled equations for the velocity at interfaces. A main distinction between the method and common numerical methods is direct solution of the velocity without discretizing flow regions, leading to smaller error. An example shows that the method is both feasible and effective.-
Keywords:
- groundwater /
- interface /
- Schwarz-Christoffel transformation.
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[1] 吕贤弼.咸淡水界面动态变化的研究.水科学进展.1991, 2: 32-41. [2] Lue Xianbi et al. Simulation of sea water intrusion in Da Xiao Ling River Fan. the XXV IAHR Congress Procedings. Tokyo. Sept. 1993: 320-327. [3] J R Chan Hong et al. the interface between fresh and salt groundwater:a numerical study. The Groundwater Numerical Simulation Symposium. Beijing, 1988. [4] J Bear. Dynamics of fluids in porous media. American Elsevier Publ.Co.1972:563-569.
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