New finite volume multiscale finite element model for simultaneously solving groundwater flow and darcian velocity fields in porous media

Abstract This paper proposes a new finite volume multiscale finite element model (NFVMSFEM) for groundwater flow and velocity simulation in porous media. The main goal of this method is to simultaneously obtain the heads and continuous x , y direction Darcian velocities, thereby simplifying the simulation process and improving the efficiency. This goal is accomplished by introducing a novel velocity matrix in the control volume boundary flux estimation of the finite volume multiscale finite element method (FVMSFEM) framework. The velocity matrix allows for the NFVMSFEM to directly represent continuous fine-scale velocities by coarse-scale heads, thus merging the two kinds of unknowns into one. Through a modified Yeh’s Galerkin model, the velocity matrix is constructed in each local coarse element before the head computation; thus, the computational cost is very little. Furthermore, the NFVMSFEM inherits the advantageous features of the FVMSFEM, which ensures the local conservation of heads and further improves the efficiency. The results of the comparison between the NFVMSFEM and certain classical methods for head and velocity computation demonstrate its effectiveness and high efficiency.