A Dimension-Reduced Line Element Method for 3D Transient Free Surface Flow in Porous Media

Abstract

In order to reduce the numerical difficulty of the 3D transient free surface flow problems in porous media, a line element method is proposed by dimension reduction. Different from the classical continuum-based methods, homogeneous permeable pores in the control volume are conceptualized by a 3D orthogonal network of tubes. To obtain the same hydraulic solution with the continuum model, the equivalent formulas of flow velocity, continuity equation and transient free surface boundary are derivable from the principle of flow balance. In the solution space of transient free surface flow, the 3D problem is transformed into 1D condition, and then a finite element algorithm is simply deduced. The greatest advantage of the line element method is line integration instead of volume/surface integration, which has dramatically decreased the integration difficulty across the jump free surface. Through the analysis of transient free surface flow in the unconfined aquifer, trapezoidal dam, sand flume and wells, the transient free surface locations predicted from the proposed line element method generally agree well with the analytical, experimental and other numerical data in the available literatures, the numerical efficiency can also be well guaranteed. Furthermore, the hydraulic anisotropy has significant effect on the evolution of free surface locations and the shape of depression cones in spatial. The line element method can be expanded to model the 3D unsaturated seepage flow, two-phase flow and thermos problems in porous media because of the similarity between the similarity of Darcy’s law, Buckingham Law and Fourier’s law.