中文摘要：

泥石流是山区多发的一种地质灾害,它的发生和发展威胁着人们的生命和财产安全,影响着人们的正常生活,因而需要加强对其发生和发展过程的研究。结合泥石流的动力模型方程采用数值模拟方法再现泥石流发生和发展的过程,是研究和预测模拟泥石流灾害的有效手段。目前的动力模型方程大多只关注动力过程,却忽视了静动力过程的统一,这将导致在一些情况下产生错误的结果。本文研究了一维泥石流的静动力阻力特征,通过修正泥石流动力学方程的阻力项,得到了具有静动力统一特征的模型方程。并以Roe格式的近似Riemann解为基础,采用MUSCL线性重构方法建立了具有较高精度和分辨率的有限体积数值求解。具体算例的数值验证表明,方程阻力项的修正是合理的,所建立的数值求解也是稳定和有效的。

英文摘要：

Debris flow is one of the common mountain hazards and seriously threatens human lives and belongings and affects society development.Therefore,it is necessary to study more about its happening and development.The approach of combining the dynamic model equations with the use of the numerical methods can lead to in-depth understanding of the development of debris flow.This is an effective approach to study and forecast the debris flow disasters.However,a majority of the present dynamic model equations focus on the dynamic process,and ignore the combination of the static and dynamic process.In fact,this neglect may result in some mis-leading results under some condition.In this paper,the characteristics of static and dynamic resistance of one-dimensional debris flow are studied.By modifying the friction resistance term of the kinetic equation,the model equation is obtained for the uniform characteristic of static and dynamic.Based on the approximate Riemann solver of Roe scheme,the numerical solution with higher precision and resolution is achieved by use of MUSCL linear reconstruction.The numerical validation of an actual example proves the rationality of the modification of friction resistance term and the stability and effectivity of the developed numerical calculation.