Analysis of transient free surface seepage flow using numerical manifold method

Abstract

In the analysis of transient seepage flow with free surfaces, not only the free surfaces but also the boundary conditions vary with time, introducing significant challenges to those traditional mesh-based numerical methods. Although the numerical manifold method (NMM) has shown great advantages in tracking time-independent free surface seepage flow due to its dual cover systems – the mathematical cover and the physical cover, in the analysis of transient free surface seepage flow it will encounter the inheritance issue of degrees of freedom between two consecutive time steps, which is still an open issue for all the partition of unity based methods such as the extended finite element method (XFEM) and the generalized finite element method (GFEM). It is shown in this study that the issue can be easily overcome if a different discretization order from the classical discretization order is adopted, i.e., time discretization is carried out before to spatial discretization. By analyzing typical transient seepage examples, the positions of the transient free surfaces predicted by the proposed method are excellently consistent with analytical solutions or experimental results. At the same time, it also points out the errors and possible consequences of some literature concerning the handling of sudden drops in upstream water level. The results demonstrate that the proposed procedure not only effectively predicts the evolution of free surfaces but also accurately addresses transient seepage problems, including those with complex drainage systems.