基于MacCormack-TVD有限差分算法的二维泥石流数值计算模型
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摘要
泥石流是一种介于崩塌滑坡和洪水之间的物理过程,既有土体的结构性,又有水体的流动性。随着泥石流运动控制方程和数值模拟技术的发展,基于数值模拟的泥石流危险性分区方法成为泥石流危险性分区的主要方法。本文应用Massflow模型,基于深度平均的连续介质力学方法,从Navier-Stokes方程出发,推导出二维运动堆积控制方程,采用MacCormack-TVD有限差分算法计算,根据古交官长沟的地形条件、水文条件、物源条件模拟了泥石流运动的全过程,计算得出泥石流泛滥范围内的流深和流速。并根据数值模拟结果和最大动能分区模型,获取该流域的泛滥范围并确定危险性分区,将模拟区划分为四个区域,即高危险区、中危险区、低危险区和安全区。泥石流的分区模型是每个网格上泥石流体的最大动能,能够直接反应泥石流对建筑物的破坏能力,分区模型具有直接的物理意义。
Debris flow is a kind of physical process between landslides and floods. Both the structure of the soil, but also the flow of water. With the development of debris flow motion control equations and numerical simulation techniques. The method of risk division of debris flow based on numerical simulation is the main method of debris flow risk zoning. In this paper, Continuum mechanics method based on depth average,starting from the Navier-Stokes equation,derived two-dimensional motion control equation of accumulation,MacCormack-TVD finite difference algorithm is used to calculated.Massflow model is used to simulate the whole process of debris flow movement according to the terrain conditions, hydrological conditions and provenance conditions of Guangou Gully in Gujiao City,calculation of debris flow inundation in the range of flow depth and velocity. And according to the results of numerical simulation and the maximum kinetic energy partition model. Obtain the flood range of the watershed and determine the risk zoning.The simulation area is divided into four zones,that is, high risk area, middle danger area, low danger area and safe area.The partition model of debris flow is the maximum kinetic energy of debris flow on each grid.It can directly reflect the damage of debris flow to buildings,so the partition model has direct physical meaning.
Debris flow is a kind of physical process between landslides and floods. Both the structure of the soil, but also the flow of water. With the development of debris flow motion control equations and numerical simulation techniques. The method of risk division of debris flow based on numerical simulation is the main method of debris flow risk zoning. In this paper, Continuum mechanics method based on depth average,starting from the Navier-Stokes equation,derived two-dimensional motion control equation of accumulation,MacCormack-TVD finite difference algorithm is used to calculated.Massflow model is used to simulate the whole process of debris flow movement according to the terrain conditions, hydrological conditions and provenance conditions of Guangou Gully in Gujiao City,calculation of debris flow inundation in the range of flow depth and velocity. And according to the results of numerical simulation and the maximum kinetic energy partition model. Obtain the flood range of the watershed and determine the risk zoning.The simulation area is divided into four zones,that is, high risk area, middle danger area, low danger area and safe area.The partition model of debris flow is the maximum kinetic energy of debris flow on each grid.It can directly reflect the damage of debris flow to buildings,so the partition model has direct physical meaning.
引文
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[19] 韦方强,胡凯衡,J.L.Lopez,等.泥石流危险性动量分区方法与应用[J].科学通报,2003,03:298-301.
[2] 王沁,姚令侃.格子Boltzmann方法及其在泥石流堆积研究中的应用[J].灾害学,2007,03:1-5.
[3] George D L,Iverson R M.A two-phase debris-flow model that includes coupled evolution of volume fractions,granular dilatancy,and pore-fluid pressure[C]// The,Intl.Conf.on Debris-Flow Hazards.2011:415-424.
[4] Mangeney-Castelnau A,Vilotte J P,Bristeau M O,et al.Numerical modeling of avalanches based on Saint Venant equations using a kinetic scheme[J].Journal of Geophysical Research Solid Earth,2003,108(B11):2527-2544.
[5] Hirt C W,Nichols B D.Volume of fluid (VOF) method for the dynamics of free boundaries ☆[J].Journal of Computational Physics,1981,39(1):201-225.
[6] Savage S B,Hutter K.The motion of a finite mass of granular material down a rough incline[J].Journal of Fluid Mechanics,2006,199(-1):177-215.
[7] Chen C,Ling C H.Continuum-Mechanics-Based Rheological Formulation for Debris Flow[C]// Hydraulic Engineering (1993).ASCE,1993.
[8] Iverson R M,Ouyang C.Entrainment of bed material by Earth‐surface mass flows:Review and reformulation of depth‐integrated theory[J].Reviews of Geophysics,2015,53(1):27-58.
[9] Denlinger R P,Iverson R M.Flow of variably fluidized granular masses across three-dimensional terrain 2.Numerical predictions and experimental tests[J].Journal of Geophysical Research Solid Earth,2001,106(B1):537-552.
[10] 唐川.泥石流数值模拟方法的探讨[J].水文地质工程地质,1994,05:9-12.
[11] 唐川,周钜乾,朱静,等.泥石流堆积扇危险度分区评价的数值模拟研究[J].灾害学,1994,04:7-13.
[12] 罗元华.泥石流堆积运动特征分析[J].地球科学,2003,05:533-536.
[13] 罗元华,陈崇希.泥石流堆积过程数值模拟及防灾效益评估方法[J].现代地质,2000,04:484-488.
[14] 胡凯衡,韦方强.基于数值模拟的泥石流危险性分区方法[J].自然灾害学报,2005,01:10-14.
[15] 胡凯衡,韦方强,何易平,等.流团模型在泥石流危险度分区中的应用[J].山地学报,2003,06:726-730.
[16] 王光谦,邵颂东,费祥俊.泥石流模拟:I—模型[J].泥沙研究,1998,03:9-15.
[17] Ouyang C,He S,Tang C.Numerical analysis of dynamics of debris flow over erodible beds in Wenchuan earthquake-induced area[J].Engineering Geology,2015,194:62-72.
[18] Ouyang C,He S,Xu Q.MacCormack-TVD Finite Difference Solution for Dam Break Hydraulics over Erodible Sediment Beds[J].Journal of Hydraulic Engineering,2014,141(5):06014026.
[19] 韦方强,胡凯衡,J.L.Lopez,等.泥石流危险性动量分区方法与应用[J].科学通报,2003,03:298-301.