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首页> 外文期刊>Applied Mathematical Modelling >Infiltration-induced phreatic surface flow to periodic drains: Vedernikov-Engelund-Vasil'ev's legacy revisited
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Infiltration-induced phreatic surface flow to periodic drains: Vedernikov-Engelund-Vasil'ev's legacy revisited

机译：渗透诱导的潜水表面流向定期排水管：Vedernikov-Engelund-Vasil'ev的遗产重新审视

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摘要

An explicit analytical solution is obtained to an old problem of a potential steady-state 2-D saturated Darcian flow in a homogeneous isotropic soil towards systematic drains modeled as line sinks (submerged drains under an overhanging of a phreatic surface), placed on a horizontal impervious substratum, with a constant-rate infiltration from the vadose zone. The corresponding boundary-value problem brings about a quarter-plane with a circular cut. A mathematical clue to solving the Hilbert problem for a two-dimensional holo-morphic vector-function is found by engaging a hexagon, which has been earlier used in analytical solution to the problem of phreatic flow towards Zhukovsky's drains (slits) on a horizontal bedrock. A hodograph domain is mapped on this hexagon, which is mapped onto a reference plane where derivatives of two holomorphic functions are interrelated via a Polubarinova-Kochina type analysis. HYDRUS2D numerical simulations, based on solution of initial and boundary value problems to the Richards equation involving capillarity of the soil, concur with the analytical results. The position of the water table, isobars, isotachs, and streamlines are analyzed for various infiltration rates, sizes of the drains, boundary conditions imposed on them (empty drains are seepage face boundaries; full drains are constant piezometric head contours with various backpressures).
机译：将显式分析解决方案获得在均匀各向同性土壤中的潜在稳态2-D饱和Darcian流程的旧问题上，朝向系统的漏极（潜伏的表面的悬垂性悬垂的垂直），放置在水平上不透水的底层，具有来自Vadose区的恒定速率浸润。相应的边值问题带来了圆形切割的四分之一平面。通过接合六边形来发现用于解决二维Holo-vercover载体功能的肝脏问题的数学线索，该方法已经早先用于分析解决方案的分析解决方案，以在水平基岩上向朱洛夫斯基的漏洞（狭缝）的潜水流的问题。映射到该六边形域，该六边形映射到参考平面上，其中通过PolubarInova-Kochina型分析相互关联两个全统称功能的衍生物。液体2D数值模拟，基于初始和边值问题的解决方案涉及土壤毛细血管的理查兹方程，同意分析结果。分析了水位，肉食，Isobars，Isotach和流线的位置，进行各种渗透率，漏极的尺寸，对它们的边界条件（空漏渗在漏洞面边界;全排水沟是恒定压电头轮廓，具有各种背压的恒定压力头轮廓）。

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