土质陡坡降雨侵蚀的数学模型及求解方法

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。

A mathematical model for rainfall erosion of steep soil slope and its solution

A mathematical models for rainfall erosion of the soil steep slope is established,which consists of the control equation of overland flow in inter-rill of soil steep slope,the control equation of water flow in rills of variable groove width of soil steep slope,the continuation equation of sediment in inter-rill of soil steep slope,and the continuity equation of sediment in rills of variable groove width of soil steep slope.Through the probability distribution of turbulent flow,the soil erosion equation is determined.The expressions of sediment source/sink terms and rill height and width are determined.To solve the model,two methods are used in combination.The finite element method is applied to discretize the mathematical model that consist of hydrodynamic equation,the motion equation,and the sediment continuity equation in space;and the finite difference method solves the problem in time domain.In this way,we could obtain the numerical calculation formula and the specific solution to the model.