MLPG法与配点法耦合求解地下水非均质承压稳定流问题  

Coupling MLPG method and collocation method for solving heterogeneous pressurized steady flow of ground water

作　　者：周德亮[1] 王宗慧 李跃 ZHOU De-liang;WANG Zong-hui;LI Yue(College of Mathmatics,Liaoning Normal University School,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院

出　　处：《吉林师范大学学报（自然科学版）》2020年第1期47-52,共6页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(61771229)

摘　　要：给出了无网格局部Petrov-Galerkin(MLPG)法与配点法耦合求解导水系数为分片常数的非均质承压稳定流问题的方法.在各子区分界线布置的节点上,应用相容条件建立配点方程组,在除分界线外的其他节点上建立MLPG方程组,联立得到求解水头函数数值解的耦合方程组.编写了相应MATLAB程序,进行了具体模型计算,并与MLPG法和边界元法的计算结果进行了比较,结果表明该方法求解问题有效,精度较MLPG法计算精度显著提高,且明显优于边界元法.A coupling method of meshless local Petrov-Galerkin(MLPG)method and the collocation method was given to solve the problem of heterogeneous pressurized steady flow,which the transmissibility coefficient were fragmentation constant.The compatible conditions were applied to set up the system of collocation equations on the nodes of each subdomain boundary arrangement,and the system of MLPG equations were established on other nodes except the subdomain boundary,and the coupled equations for solving the numerical solution of the head function were obtained simultaneously.The corresponding MATLAB program was written and the concrete model calculation was carried out,compared with the results of MLPG method and boundary element method,the results show that the method is effective in solving the problem,and the accuracy is significantly higher than that of MLPG method,moreover,it is obviously better than the boundary element method.

关 键 词：MLPG 配点法 非均质 相容条件 移动最小二乘法 

分 类 号：O242[理学—计算数学]