Abstract: Richards equation is the fundamental equation in unsaturated seepage theory. It is commonly solved using numerical methods combined with effective iterative techniques. Time step adjustment methods are frequently used to enhance computational efficiency. To investigate the numerical performance of different adaptive time step methods, a finite element procedure employing the FEM combined with the adaptive relaxed Picard method and adaptive time step methods was developed. The effects of different adaptive time step methods on the computational accuracy and efficiency were assessed through simulations of unsaturated seepage problems. The results demonstrate that the developed procedure is practical and reliable, and it can guarantee the stability even when the time step changes significantly; the heuristic method is simple and efficient but may struggle to ensure high computational accuracy in problems with challenging iterative convergence; the numerical performance of the truncation error method is influenced by the truncation error threshold, with a smaller threshold leading to higher accuracy but lower efficiency, while a larger threshold resulting in lower accuracy but higher efficiency, and by adjusting the threshold, the truncation error method can achieve a better balance between computational accuracy and efficiency. The research findings are valuable for advancing and applying efficient unsaturated seepage finite element programs.

Key words: unsaturated seepage, finite element method, adaptive time step method, truncation error method, heuristic method