MQ点插值法在地下水稳定流计算中的应用

Multi-quadric（MQ）点插值法是一种求解偏微分方程的新方法。为探讨该方法在地下水稳定流问题中的应用效果，及MQ函数的形状参数、支持域大小、场节点间距对计算结果的影响，将该方法分别用于参数不变的二维地下水稳定流动、参数连续变化的二维地下水稳定流动和地下水向承压完整井的稳定流动3种算例的求解中，并将计算结果与解析解进行比较。结果表明该方法求解二维稳定流问题时具有较好的效果。MQ函数的形状参数、场节点间距和支持域大小对计算结果的误差具有较大影响。

Application of multi-quadric method for numerical simulation of steady groundwater flow

Multi-quadric (MQ) interpolation is a new numerical method to solve partial differential equations (PDEs). The purpose of this paper was to discuss the effectiveness of the method applied to simulate groundwater flow, and the influence of shape parameters, support domain, node spacing on results. We used MQ method for the numerical solution of three cases of 2D steady groundwater flow. Case one was a flow in a confined aquifer with constant coefficient of transmissivity (T), while case two was with T varying continuously. Case three represented the flow to a fully penetrated pumping well in a confined aquifer. The method was found to have good agreement with exacted solution of the three cases. The error was affected by the combination of function parameters of MQ method, size of support-domain, and node spacing.