Research papersEfficient triple-grid multiscale finite element method for 3D groundwater flow simulation in heterogeneous porous media

- ETMSFEM introduces a new 3D linear base function to construct base function.
- ETMSFEM employs domain decomposition technique to construct base function.
- Based on Yeh's theory, ETMSFEM can efficiently obtain continuous Darcian velocity.
- ETMSFEM is much more efficient than FEM and MSFEM in head computation.
- ETMSFEM is much more efficient than Yeh's Galerkin model in velocity computation.

In this paper, an efficient triple-grid multiscale finite element method (ETMSFEM) is proposed for 3D groundwater simulation in heterogeneous porous media. The main idea of this method is to employ new 3D linear base functions and the domain decomposition technique to solve the local reduced elliptical problem, thereby simplifying the base function construction process and improving the efficiency. Furthermore, by using the ETMSFEM base functions, this method can solve Darcy's equation with high efficiency to obtain a continuous velocity field. Therefore, this method can considerably reduce the computational cost of solving for heads and velocities, which is crucial for large-scale 3D groundwater simulations. In the application section, we present numerical examples to compare the ETMSFEM with several classical methods to demonstrate its efficiency and effectiveness.