节水灌溉Issue(1)：41-53,62,14.DOI:10.12396/jsgg.2025220
Richards方程数值求解方法的研究进展、挑战与未来展望
Numerical Solution Methods for Richards'Equation:Progress,Challenges,and Future Prospects
摘要
Abstract
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.关键词
Richards方程/高精度/离散化/迭代/数值求解Key words
Richards equation/high accuracy/discretization/iteration/numerical solution分类
农业科技引用本文复制引用
杨思琪,李小纲,梅力方,乔潘诗霈,马轶..Richards方程数值求解方法的研究进展、挑战与未来展望[J].节水灌溉,2026,(1):41-53,62,14.基金项目
国家自然科学基金项目(52369015) （52369015）
宁夏高等学校一流学科建设(水利工程)项目(NXYLXK2021A03) （水利工程）
宁夏重点研发引才专项(2024BEH04095). （2024BEH04095）
