不规则区域溶质迁移问题的局部径向基函数算法研究

Research on local radial basis function algorithms for solute transport problems in irregular domains

地下水污染物迁移的数值模拟能为地下水体污染防治提供科学依据,具有重要的意义。结合局部径向基函数法与有限差分法求解不规则区域中溶质迁移问题。局部径向基函数法不同于传统的全局径向基函数法,仅需通过位于配置点周围子域内的邻近节点来构造插值矩阵,可以有效避免全局径向基函数法计算大规模矩阵时矩阵病态及对形状参数敏感的问题,提高了数值解的精确性和稳定性。通过数值算例验证了算法在处理不规则区域问题上的有效性,并分析了形状参数、总节点数、子域节点数、布点方式和边界形状等因素对算法精确性和鲁棒性的影响。

Numerical simulation of groundwater contaminant migration can provide a scientific basis for groundwater pollution prevention and control with great significance.This paper combines the local radial basis function method with the finite difference method for solving solute transport in irregular domains.Compared with the traditional global radial basis function method,the local radial basis function method only needs the adjacent nodes located in the sub-domains to construct the interpolation matrix.This can effectively avoid the problems of matrix pathology and sensitivity to shape parameters when calculating large matrices by the global radial basis function method and improve the accuracy and stability of the numerical solution.Numerical examples are used to verify the effectiveness of the proposed algorithm in dealing with the problems with irregular domains.In addition,the influence of the shape parameter,the number of total nodes,the number of nodes in the subdomain,the distribution pattern and the boundary shape on the accuracy and robustness of the algorithm is analyzed.