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

•The NFVMSFEM can compute continuous x, y directional velocities and heads simultaneously.•The NFVMSFEM is a combination of the FVM, MSFEM and Yeh’s FEM, based on the FVMSFEM.•The NFVMSFEM velocity matrixes can present velocity unknowns by head unknowns.•The NFVMSFEM achieves a high computation efficiency.