泥石流的二维数学模型

泥石流是在重力作用下，由砂粒石块和水等组成的固液混合物，是一种发生于山区的复杂的地质灾害现象。泥石流主要是由暴雨诱发引起的，它沿着复杂的三维地形高速流动，具有流体流动的特性。为了模拟泥石流的运动规律，预测降雨诱发的泥石流的到达距离和泛滥范围，减少和避免泥石流引起的灾害，把泥石和雨水组成的固液混合物假定为遵循均匀、连续、不可压缩的、非定常的牛顿流体运动规律。基于质量守恒方程和Naiver-stokes方程，采用深度积分方法，推导出了一个模拟泥石流运动的二维数学模型。所有方程式可用有限差分法来求解。结合GIS，该模型可用于预测泥石流的流动距离和泛滥范围，以及泛滥范围内的危险房屋和路段，也可以用于泥石流灾害的风险性分析。

Two-dimensional mathematical model of debris flow

Debris flow is the gravity flow of water, clay, granular and rock mixtures and often triggered by torrential rains in mountainous areas. It is a catastrophic disaster that consists of grain-fluid mixtures and moves rapidly across three-dimensional terrain. Most debris flows move downslope as fluids. To predict the runout distance and extent of the hazard area of rainfall-induced debris flows, we proposed a depth-averaged two-dimensional mathematical model, in which the debris and water mixture is assumed to be uniform continuous, incompressible, unsteady Newtonian turbulence fluid. Based on mass balance equation and Navier-Stokes equations, the mathematical model is derived using the method of depth-integrated equations. The finite difference method is necessary to solve the all equations. Based on GIS, the two-dimensional mathematical model of debris flow can be used to estimate the flow range, the potentially dangerous homes and roads for hazard and risk analysis.