Variably saturated flow theory is the fundamental theory of geotechnical engineering; and it has wide applications to seepage of earth rockfill dam

contaminant transport

seepage and phase transformation of frozen soil

and slope stability analysis. In numerical solution of Richards equation for variably saturated flow

inappropriate computation of some parameters

particularly for the hydraulic conductivity

may lead to convergence oscillation of nonlinear iterative methods such as Picard method or Newton method

and consequently result in slow convergence and inaccurate solution. To eliminate or reduce the influence of iterative convergence oscillation

the under-relaxation method is often employed. By using 1D problem and 2D heterogeneous earth dam

the limitations of available under-relaxation methods are demonstrated. Furthermore

a novel short-term mixed under-relaxation method is proposed with verified practicability and reliability.