求解非均质渗流场的改进数值流形方法

An improved numerical manifold method for solving heterogeneous seepage problem

精确的流速场计算是模拟非均质多孔介质渗流、溶质运移以及污染物迁移等过程的基础。常规方法计算得到流速场精度低、连续性差。高阶流形方法可以显著提高流速场计算精度,但对于高水力梯度问题,流速场依然是不连续的,且常常伴随着线性相关问题,导致求解精度降低,甚至求解失败。针对这一问题,采用两种改进的权函数构造流形单元上的总体近似函数,编制相应的程序,消除高阶覆盖函数带来的线性相关问题,且分别得到节点连续和全局连续的流速/梯度解。通过若干算例对改进权函数程序的收敛性和精度进行分析。

An accurate velocity filed is important for simulating Darcy flow,solution transport and contaminant migration in heterogeneous porous media.Generally,the velocity results calculated by the conventional numerical methods have low precision and poor continuity.To overcome this defect,two improved weight functions are used to construct the global approximation on manifold elements and two improved NMM codes are developed to eliminate the linear dependence problems caused by the higher-order overburden functions,and the velocity/gradient solutions of node continuity and global continuity are obtained,respectively.Furthermore,the convergence and accuracy of the improved weight function NMM codes are analyzed through several examples.