一种模拟节点达西渗透流速的双重网格多尺度有限单元法

A dual-mesh multiscale finite element method for simulating nodal Darcy velocities in aquifers

提出了一种用于模拟节点达西渗透流速的双重网格多尺度有限单元法(D-MSFEM)。该方法是多尺度有限单元法(MSFEM)与VedatBatu双重网格技术(D-FEM)的有机结合,不仅可以应用双重网格技术获得连续、精确的水头一阶导数,还可以应用多尺度基函数直接在粗网格上求解水头和达西渗透流速,从而突破了传统有限元基础框架的限制,具有极高的计算效率。同时,D-MSFEM还可以应用粗尺度节点的达西渗透流速和多尺度基函数直接获得细尺度节点的达西渗透流速,而无需在精细尺度上求解,能够节约大量的计算消耗。应用D-MSFEM和多种传统达西渗透流速计算方法对地下水稳定流和非稳定流进行了模拟,结果显示D-MSFEM具有极高的模拟效率和精度。该方法可为高效计算地下水达西渗透流速问题提供新途径。

A dual-mesh multiscale finite element method(D-MSFEM)is developed to simulate nodal Darcy velocities in aquifers.It is a combination of the multiscale finite element method(MSFEM)and the dual-mesh finite element method(D-FEM).D-MSFEM can obtain continuous first-order head derivatives and solve the head and nodal Darcy velocities directly on the coarse grid without the necessity for solving Darcy equation specifically.Therefore,it breaks through the limitations of the traditional finite element basic framework and improves the computational efficiency extremely in comparison to the traditional methods for nodal Darcy velocities.D-MSFEM can also directly obtain the fine-scale nodal Darcy velocities by using the coarse-scale nodal Darcy velocities and the multiscale base functions,which can save a lot of computational cost.D-MSFEM is compared with some traditional methods for nodal Darcy velocities in the simulation of groundwater steady flow and transient flow.The results show that D-MSFEM achieves higher simulation efficiency and accuracy.This study may provide a new approach to simulate nodal Darcy velocities in aquifers efficiently.