The Analysis And The Computation For Richards’ Equation During The Infiltration Process In Saturated And Unsaturated Soil

Richards’ equation is the governing equation during the infiltration process in soil. Soil is heterogeneity and the hydraulic conductivity is non- linear highly.The boundary conditions and initial conditions are always complexly. All of these properties make it di?cult to get the numerical solution. The traditional finite- di?erence and finite- element solutions to Richards’ equation can exhibit non- physics numerical oscillation. It is important to Soil Hydrodynamics to find the e?ective solutions of Richards’ equation. The main findings of the study are summarized as follows.The soil constitutive relation on the layered- interface is changed which makes the hydraulic conductivity and the soil water content are discontinuous.For a class of Gardener- Basha Richards’ equation describing layered soil, to avoid the numerical oscillation on the layered- interface, we give a method to get the semi- analytical solution. By analyzing the constitutive relation on the layered interface and discreting temporal dimension, we get the iterative scheme and get the semi-analytical. The parallel scheme for this method is designed. The parallel speedup ratio is 4.392 through numerical experiments.For the numerical oscillation in transient flow phenomenon, we improve the accuracy of basis function and make the numerical solution smooth in whole?. Meanwhile, adaptive mesh generation is used. To meet the requirements of smoothness, Cubic spline basis EFM is used in one dimension and Hermit interpolation function with 5 order is used in two dimensions. This method makes the oscillation eased.The long- time phenomenon is described by Richards’ equation. Structure preserving algorithm on temporal dimension can improve the stability of numerical solution significantly. Implicit symplectic Runge- Kutta method of s- stage and2s- order is used to discrete temporal dimension. The numerical experiments show that the solution with this method apperas long-term stability more better.We give the calculating scheme for the model coupled heat transport and variably saturated water flow in frozen soil. This model is concerned by the project that my mentor joined. Up to now, the calculating scheme for this model is based on the combination of implicit Euler method and linear Finite Element Method.We analysis and sort the constitutive relations and the boundary conditions and initial conditions, design the calculating scheme. Through the numerical experiments, the calculating scheme for this model has been shown to be e?ective.The parallel calculating scheme for numerical solution is very important.We give the total calculation amount of the schemes designed by us. For getting the resolves of linear equations parallely, the method of column pivot with double loops is presented. This method is superior to the traditional row- partition and column- partition method in communication time, degree of parallelism and scalability. The numerical experiments based on this parallel calculating scheme shows the parallel speedup ratio is 3.461.