New Finite Volume–Multiscale Finite-Element Model for Solving Solute Transport Problems in Porous Media

Abstract

This paper proposes a finite volume–Yeh’s finite-element–multiscale finite-element model (FVYMSFEM) for solute transport simulations, which is extended from its elliptic groundwater-flow equation scheme. The primary goals of this method are to compute advection-dominated advection-dispersion equation with high accuracy and high efficiency and to obtain continuous dispersion velocity together with concentration. The finite volume integration scheme allows the FVYMSFEM to substantially reduce the numerical dispersion and ensures local mass conservation, thus to effectively deal with a high Peclet number in advection-dominated case. Meanwhile, due to the combination of the Crank-Nicolson format and finite volume scheme, the FVYMSFEM can achieve high accurate solutions with a large time step under advection-dominated condition, even with a high Courant number. Moreover, the FVYMSFEM introduces a novel dispersion velocity matrix to transform the concentration and continuous dispersion velocity into each other, thus to calculate them in once computation. The FVYMSFEM control volume boundary flux inherits the continuity of the dispersion velocity, which leads to higher solution accuracy. In addition, similar to the multiscale finite-element method (MSFEM), the FVYMSFEM can compute solutions in a coarse-scale grid without resolving all the fine-scale features, thus saving computational effort. Some results indicate that the FVYMSFEM is more accurate than the MSFEM and conventional linear basis function finite-element method (LFEM) in advection-dominated cases. Furthermore, the FVYMSFEM can achieve the same number of concentrations as the fine grid LFEM (LFEM-F) with close accuracy while saving more than 99.8% CPU time.