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建立了土质陡坡降雨侵蚀的数学模型,模型包括陡坡细沟间坡面流控制方程、变沟宽陡坡细沟流控制方程、陡坡细沟间坡面侵蚀泥沙连续方程及陡坡变沟宽细沟侵蚀泥沙连续方程。通过紊流冲击分布概率确定土壤剥蚀方程,确定了泥沙源/汇项的表达形式及细沟高程与宽度的表达式。通过有限元和有限差分相结合的方法求解该数学模型,利用有限单元法对数学模型的水动力方程、运动方程及泥沙连续方程进行空间上的离散,利用有限差分法解决时间域的问题,得出了顺序求解的数值计算公式及模型数值求解的具体方法和步骤。
The mathematical model of rainfall erosion on steep slopes is established. The model includes the slope flow control equation of steep slopes, the governing equation of steep slopes of variable width ditch, the continuous equation of erosion and sediment on slopes of steep slopes, Erosion Sediment Continuous Equation. The denudation equation of soil is determined by the probability of turbulence impact distribution, and the expression of sediment source / sink term and the expression of the height and width of the flume are determined. The finite element method and the finite difference method are used to solve the mathematical model. The finite element method is used to discretize the hydrodynamic equation, the motion equation and the sediment continuous equation of the mathematical model. The finite difference method is used to solve the problem of time domain. The numerical calculation formula of sequential solving and the specific methods and steps of numerical solution of the model are obtained.