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

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.