用最小二乘配点法解地下水稳定流问题

Application of Least-square Collocation Meshless Method in Simulation of Steady Groundwater Flow

最小二乘配点无网格法是一种新型高效的无网格法。该方法除节点外又在研究域内引入辅助点,近似函数仍然只通过节点构造,微分方程在所有节点和辅助点上满足。本文将最小二乘配点无网格法应用于非均质多孔介质中的二维地下水稳定流问题,推导了计算格式、编制了相应的计算程序。算例结果表明,最小二乘配点无网格法算法简单,有较高的精度且节省计算量。

The Least square collocation meshless method is a new type of highly efficient meshless method. Except for nodes, a number of auxiliary points are introduced into the research field. Approximation functions are still structured using the nodes, differential equations are satisfied in all nodes and auxiliary points. This method is applied to numerically simulate the 2 - D steady groundwater flow in heterogeneous porous media and the corresponding computer program is developed. The result shows that algorithm of the method is simple and have high accuracy and calculation speed.