Unsaturated soil seepage analysis using temporal adaptive transformation method with under-relaxation

This research tends to develop robust numerical methods for solving the highly nonlinear partial differential equation describing unsaturated soil flow. Based on the research of a modified transformation method with under-relaxation, the numerical performance of this promising method with automatic temporal adaptive scheme is investigated. Example shows that such a combination approach can be a robust numerical method for practical unsaturated flow simulations, as it provides the most efficient solution at minimal computational cost; its performance is rather robust with moderate changes of several parameters introduced; and it is conceptually and computationally simple which can be easily incorporated into existing software codes based on the backward Euler scheme.