Abstract
In this paper, we propose the meshless finite point method for solving a type of fluid flow problem. The moving least square function is combined with the collocation method to treat nonlinear one- and two-dimensional soil water-salt movement equations. An adaptive windward scheme is used to stabilize the numerical solution in regions with a large gradient change. Numerical examples with the comparison among the proposed method, finite element method and characteristic finite element method show that the meshless finite point method is more accurate and is used to eliminate the numerical oscillation phenomenon.
Highlights
Soil salinization caused by unreasonable irrigation has become a major bottleneck restricting the sustainable development of agriculture [1]
The purpose of this paper is to study the law of water and salt migration under the conditions of water infiltration, the accuracy and validity of this algorithm are verified by practical problems, which provides a scientific basis for reasonable irrigation
4 Conclusions Through fully discussing the effects of support domain size, node number and time step size on the simulation results, it can be concluded that the number of nodes has a direct impact on the calculation accuracy
Summary
Soil salinization caused by unreasonable irrigation has become a major bottleneck restricting the sustainable development of agriculture [1]. The rational development of inferior water resources and the improvement of the utilization of saline-alkali land and soil water have become an issue of focus which all countries are concerned about. Studying the process of soil water-salt balance migration and carrying out quantitative numerical simulations of an appropriate mathematical model provide the necessary foundation for monitoring, evaluating and controlling soil salinization in arid areas. It is important to prevent the accumulation of salinity, the loss of water and soil resources, and the desertification of land. It is necessary to save water, make irrigation, and increase production and income. As early as the 1960s, the research on the movement of water and salt has gradually developed from simple matter balance calculation to mathematics and computer simulations, which makes the concept of water and salt movement clearer and more quantitative. The numerical simulation can set the initial and boundary conditions flexibly, it can describe the process of water and salt mi-
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