Richards方程数值求解方法的研究进展、挑战与未来展望OA

Water movement in unsaturated porous media is a focal point of concern in multiple disciplines,including hydrology,agriculture,and environmental engineering.The Richards equation,as a crucial mathematical equation for describing this phenomenon,plays an essential role in advancing our understanding of soil water movement.The equation has three distinct forms and reveals the nonlinear relationships among related variables through soil constitutive relationships.Numerical methods have emerged as the primary approach for solving the Richards equation,achieving significant advancements progress in its solution over the course of several decades.To deepen the fundamental understanding of this field and propel related research forward,this paper systematically reviews the evolution of the Richards equation and,focusing on the spatial discretization methods,temporal discretization methods,and iterative methods employed in solving this equation,along with the existing solution models and codes.Additionally,this paper also summarizes the principal problems and challenges currently encountered in solving the Richards equation and explores and anticipates future research directions and practical application prospects,aiming to foster the further advancement of this field.