格子Boltzmann方法理论及其在泥石流研究中的应用
|
摘要
泥石流是普遍存在于山区的一种突发性自然现象。它是不同于通常的牛顿流体，运动过程呈现非线性的特殊流体。格子Boltzmann方法，作为一种从微观领域出发的求解流体力学问题的新数值方法，可能成为求解泥石流这一类特殊流体力学问题的全新方法。
本文根据泥石流的非线性特征以及泥石流入汇主河的实验结果，对平衡态分布函数、非平衡态函数等Boltzmann模型因子进行了改造，建立了几种各具特色的格子Boltzmann模型，成功模拟了泥石流的一维运动过程，二维堆积过程，以及泥石流入汇主河的过程。
本文的工作主要包括：
1、针对泥石流的非线性特征，以及泥石流入汇主河的复杂性，从格子Boltzmann方法的理论可以看出：格子气方法不适合应用于泥石流的研究，格子BGK方法用于泥石流及泥石流入汇主河的研究具有一定的可行性；增强碰撞算子格子Boltzmann方法用于泥石流及泥石流入汇主河的研究，必须对其进行改造和创新。
2、通过求解Burgers方程、求解一维水击现象的偏微分方程组，以及模拟主河清水的运动，探讨了格子Boltzmann方法在牛顿流体中的应用。从建立上述三个格子Boltzmann模型可以看出：如何构造平衡态分布函数，使其反映了流体运动的非线性特征，是建立合理的泥石流格子Boltzmann模型的核心问题。
3、针对一维粘性泥石流的运动过程和二维泥石流堆积过程，设计了两种格子Boltzmann模型：(1)设计了平衡态分布函数是泥深和速度的非线性函数的一维格子Boltzmann模型，该模型成功获得了不同断面的水深和流速随时间的变化曲线；(2)设计了非平衡态分布函数是泥深和流速梯度的线性函数的二维格子Boltzmann模型，该模型成功获得了堆积扇横剖面分层结构图，模拟了泥石流的堆积过程。
4、针对泥石流入汇主河，开展多组入汇角度不同的模型实验。从模型实验现象可以看出：(1)主河与泥石流支沟的流量比、主河水流的速度、以及入汇角度等因素对泥石流入汇主河相互作用机制的影响；(2)入汇角为45°时泥石流与主河交汇的流动特性，与90°交汇时的流动特性有本质不同；(3)入汇角为30°时泥石流与主河交汇的流动特性，与60°交汇时的流动特性具有相似性。实验现象表明：针对垂直主河方向的速度与顺主河方向流速差异不同应建立不同的格子Boltzmann模型；主河清水不仅对泥石流运动速度具有影响，而且对泥石流结构造成破坏，在处理过程中具有一定的困难和复杂性。
5、针对垂直主河方向的速度与顺主河方向流速差异，以及主河清水的处理方式，设计了不同的格子Boltzmann模型：(1)设计了平衡态分布函数是速度、密度、动量梯度的非线性函数的格子Boltzmann模型，该模型成功模拟了90°交汇时泥石流入汇主河的过程，为研究泥石流入汇主河的运动机理提供一种新手段。(2)设计了混合格子Boltzmann模型，该模型模拟45°时泥石流入汇主河的现象，为分析不同角度下泥石流入汇主河的相互机制提供一种新手段。(3)对空间引入旋转变换，建立了映射格子Boltzmann模型，该模型模拟了30°交汇时和60°交汇时泥石流入汇主河的现象，从而了解不同入汇角度下泥石流入汇主河的相互作用机制。(4)考虑主河清水对泥石流运动速度和对泥石流结构的影响，本文还提出了一个新模型——双分布函数的格子Boltzmann模型。通过与相应的室内实验进行对比，可以看出双分布格子Boltzmann模型反映了不同空间不同时间主河清水对泥石流结构的破坏和速度的影响。
Debris flow is unexpected natural phenomenon which is commonly found in a mountainous area, whose movement process is non-linear. As a new numerical method of solving the fluid mechanics problems from the field of micro-dynamics, the lattice method may become a new method successfully simulated the nonlinear characteristic of debris flow.
In this paper, based on the nonlinear characteristic of debris flow and the experimental results of debris flow ingoing the primary river, carried on some reformation to some the Boltzmann model's factors for example the equilibrium distribution function, the non-equilibrium distribution function etc, several characteristics lattice Boltzmann models were set up successfully simulated debris flow's one-dimensional movement, two-dimensional deposition and debris flow ingoing the primary river.
The main work and conclusions were as follows:
1、In view of non-linear characteristics of debris flow and debris flow into the main river of complexity, the conclusions can be drew from the theory of lattice Boltzmann method: the lattice gas method is not suitable for debris flow ; the Lattice BGK method for debris flow and debris flow ingoing the primary river is a feasibility study; Lattice Boltzmann method with enhanced collisions for debris flow and debris flow ingoing the primary river need for some transformations and innovations.
2、Through solving the Burgers equation, solving one dimension partial-differential equations of the water hammer phenomenon, and simulating the fluid flow in the primary river, the lattice Boltzmann method's application to the Newton fluid flow were studied. From the establishment of the above three lattice Boltzmann models the conclusions can be drew: It is the core of the problem for establishing lattice Boltzmann models of debris flow, how to construct the equilibrium distribution function reflected the characteristics of the nonlinear movement.
3、Aimed at debris flow's one-dimensional movement and two-dimensional deposition, two lattice Boltzmann models were established : (1) A Boltzmann models was established whose equilibrium distribution function is a nonlinear function of depth and velocity of debris flow. Under the lattice Boltzmann model, one-dimension movement of debris flow was simulated, and the spatial and temporal variations of depth and velocity were obtained. (2) A Boltzmann model was established whose non-equilibrium distribution function is a linear function of depth and velocity gradient of debris flow. Under the lattice Boltzmann model, the deposition of debris flow was simulated, and the layered configuration of deposit sector of the debris flow was obtained.
4、Aimed at the confluence between debris flow and the primary river, the group experiments were conducted. Based on analyzing the experimental phenomena, some conclusions can be seen: (1) some factors for example the ratio of the primary river flux to the debris flow flux, the velocity of the primary river, the ingoing angle etc affect the mechanism of confluence;(2) the mechanism of confluence at ingoing angle 45°is different from the mechanism of the debris flow ingoing the primary river at ingoing angle 90°in essence ;(3) the mechanism of confluence at ingoing angle 30°is similar to the mechanism of the debris flow ingoing the primary river at ingoing angle 60°;(4) the primary river not only has an impact on the debris flow velocity, but on damage configuration of debris flow .there are a lot of difficulty and complexity in dealing with the infection of the primary river.
5、Based on the differences of he vertical direction of the primary river velocity between the parallel direction of the primary river velocity ,and different approach of dealing with the infection of the primary river, some lattice Boltzmann model were set up: (1) A Boltzmann models was established whose equilibrium distribution function is a nonlinear function of density ,velocity and momentum gradient of debris flow. Under the lattice Boltzmann model, the debris flow ingoing primary river at ingoing angle 90°is simulated, the result accord with basically the result of experiment which provides a new method for studying movement mechanisms of the confluence between debris flow and the main river. (2) The combined lattice Boltzmann model is set up, which succeed in simulating the debris flow ingoing primary river at ingoing angle 45°, providing a new means for analyzing reciprocity mechanisms of the confluence between debris flow and the main river at different ingoing angle.(3) Use of the rotation of space, the mapping lattice Boltzmann model is set up. Which succeed in simulating the debris flow ingoing primary river at 60°and 30°, which make quantity surveyors realize the different reciprocity mechanisms at different ingoing angle. (4)On account of the fluid flow in the primary river affect the velocity and configuration of the debris flow after confluence, the double equilibrium distributing lattice Boltzmann model are established, which succeed in depicting different infection of the fluid flow on debris flow in differ time and differ space.
本文根据泥石流的非线性特征以及泥石流入汇主河的实验结果，对平衡态分布函数、非平衡态函数等Boltzmann模型因子进行了改造，建立了几种各具特色的格子Boltzmann模型，成功模拟了泥石流的一维运动过程，二维堆积过程，以及泥石流入汇主河的过程。
本文的工作主要包括：
1、针对泥石流的非线性特征，以及泥石流入汇主河的复杂性，从格子Boltzmann方法的理论可以看出：格子气方法不适合应用于泥石流的研究，格子BGK方法用于泥石流及泥石流入汇主河的研究具有一定的可行性；增强碰撞算子格子Boltzmann方法用于泥石流及泥石流入汇主河的研究，必须对其进行改造和创新。
2、通过求解Burgers方程、求解一维水击现象的偏微分方程组，以及模拟主河清水的运动，探讨了格子Boltzmann方法在牛顿流体中的应用。从建立上述三个格子Boltzmann模型可以看出：如何构造平衡态分布函数，使其反映了流体运动的非线性特征，是建立合理的泥石流格子Boltzmann模型的核心问题。
3、针对一维粘性泥石流的运动过程和二维泥石流堆积过程，设计了两种格子Boltzmann模型：(1)设计了平衡态分布函数是泥深和速度的非线性函数的一维格子Boltzmann模型，该模型成功获得了不同断面的水深和流速随时间的变化曲线；(2)设计了非平衡态分布函数是泥深和流速梯度的线性函数的二维格子Boltzmann模型，该模型成功获得了堆积扇横剖面分层结构图，模拟了泥石流的堆积过程。
4、针对泥石流入汇主河，开展多组入汇角度不同的模型实验。从模型实验现象可以看出：(1)主河与泥石流支沟的流量比、主河水流的速度、以及入汇角度等因素对泥石流入汇主河相互作用机制的影响；(2)入汇角为45°时泥石流与主河交汇的流动特性，与90°交汇时的流动特性有本质不同；(3)入汇角为30°时泥石流与主河交汇的流动特性，与60°交汇时的流动特性具有相似性。实验现象表明：针对垂直主河方向的速度与顺主河方向流速差异不同应建立不同的格子Boltzmann模型；主河清水不仅对泥石流运动速度具有影响，而且对泥石流结构造成破坏，在处理过程中具有一定的困难和复杂性。
5、针对垂直主河方向的速度与顺主河方向流速差异，以及主河清水的处理方式，设计了不同的格子Boltzmann模型：(1)设计了平衡态分布函数是速度、密度、动量梯度的非线性函数的格子Boltzmann模型，该模型成功模拟了90°交汇时泥石流入汇主河的过程，为研究泥石流入汇主河的运动机理提供一种新手段。(2)设计了混合格子Boltzmann模型，该模型模拟45°时泥石流入汇主河的现象，为分析不同角度下泥石流入汇主河的相互机制提供一种新手段。(3)对空间引入旋转变换，建立了映射格子Boltzmann模型，该模型模拟了30°交汇时和60°交汇时泥石流入汇主河的现象，从而了解不同入汇角度下泥石流入汇主河的相互作用机制。(4)考虑主河清水对泥石流运动速度和对泥石流结构的影响，本文还提出了一个新模型——双分布函数的格子Boltzmann模型。通过与相应的室内实验进行对比，可以看出双分布格子Boltzmann模型反映了不同空间不同时间主河清水对泥石流结构的破坏和速度的影响。
Debris flow is unexpected natural phenomenon which is commonly found in a mountainous area, whose movement process is non-linear. As a new numerical method of solving the fluid mechanics problems from the field of micro-dynamics, the lattice method may become a new method successfully simulated the nonlinear characteristic of debris flow.
In this paper, based on the nonlinear characteristic of debris flow and the experimental results of debris flow ingoing the primary river, carried on some reformation to some the Boltzmann model's factors for example the equilibrium distribution function, the non-equilibrium distribution function etc, several characteristics lattice Boltzmann models were set up successfully simulated debris flow's one-dimensional movement, two-dimensional deposition and debris flow ingoing the primary river.
The main work and conclusions were as follows:
1、In view of non-linear characteristics of debris flow and debris flow into the main river of complexity, the conclusions can be drew from the theory of lattice Boltzmann method: the lattice gas method is not suitable for debris flow ; the Lattice BGK method for debris flow and debris flow ingoing the primary river is a feasibility study; Lattice Boltzmann method with enhanced collisions for debris flow and debris flow ingoing the primary river need for some transformations and innovations.
2、Through solving the Burgers equation, solving one dimension partial-differential equations of the water hammer phenomenon, and simulating the fluid flow in the primary river, the lattice Boltzmann method's application to the Newton fluid flow were studied. From the establishment of the above three lattice Boltzmann models the conclusions can be drew: It is the core of the problem for establishing lattice Boltzmann models of debris flow, how to construct the equilibrium distribution function reflected the characteristics of the nonlinear movement.
3、Aimed at debris flow's one-dimensional movement and two-dimensional deposition, two lattice Boltzmann models were established : (1) A Boltzmann models was established whose equilibrium distribution function is a nonlinear function of depth and velocity of debris flow. Under the lattice Boltzmann model, one-dimension movement of debris flow was simulated, and the spatial and temporal variations of depth and velocity were obtained. (2) A Boltzmann model was established whose non-equilibrium distribution function is a linear function of depth and velocity gradient of debris flow. Under the lattice Boltzmann model, the deposition of debris flow was simulated, and the layered configuration of deposit sector of the debris flow was obtained.
4、Aimed at the confluence between debris flow and the primary river, the group experiments were conducted. Based on analyzing the experimental phenomena, some conclusions can be seen: (1) some factors for example the ratio of the primary river flux to the debris flow flux, the velocity of the primary river, the ingoing angle etc affect the mechanism of confluence;(2) the mechanism of confluence at ingoing angle 45°is different from the mechanism of the debris flow ingoing the primary river at ingoing angle 90°in essence ;(3) the mechanism of confluence at ingoing angle 30°is similar to the mechanism of the debris flow ingoing the primary river at ingoing angle 60°;(4) the primary river not only has an impact on the debris flow velocity, but on damage configuration of debris flow .there are a lot of difficulty and complexity in dealing with the infection of the primary river.
5、Based on the differences of he vertical direction of the primary river velocity between the parallel direction of the primary river velocity ,and different approach of dealing with the infection of the primary river, some lattice Boltzmann model were set up: (1) A Boltzmann models was established whose equilibrium distribution function is a nonlinear function of density ,velocity and momentum gradient of debris flow. Under the lattice Boltzmann model, the debris flow ingoing primary river at ingoing angle 90°is simulated, the result accord with basically the result of experiment which provides a new method for studying movement mechanisms of the confluence between debris flow and the main river. (2) The combined lattice Boltzmann model is set up, which succeed in simulating the debris flow ingoing primary river at ingoing angle 45°, providing a new means for analyzing reciprocity mechanisms of the confluence between debris flow and the main river at different ingoing angle.(3) Use of the rotation of space, the mapping lattice Boltzmann model is set up. Which succeed in simulating the debris flow ingoing primary river at 60°and 30°, which make quantity surveyors realize the different reciprocity mechanisms at different ingoing angle. (4)On account of the fluid flow in the primary river affect the velocity and configuration of the debris flow after confluence, the double equilibrium distributing lattice Boltzmann model are established, which succeed in depicting different infection of the fluid flow on debris flow in differ time and differ space.
引文
[1] C．M．弗莱施曼著，姚德基译．泥石流[M]．科学出版社，1986，1-10．
[2] 田连权，张信宝，吴积善．试论泥石流的形成过程[M]．泥石流文集(1)，科技文献出版社重庆分社，1981，54-59．
[3] 池谷浩，土石流的分类[J]．土木技术资料，1978，20(3)，323-325．
[4] 钱宁，王兆印．泥石流运动机理的初步探讨[J]．地理学报，1984，39(1)，33-43．
[5] 章书成，泥石流研究评述[J]．力学进展，1989，13(3)，365-374．
[6] 李德基主编，泥石流减灾理论与实践[M]．科学出版社，1997，31-32．
[7] 中国科学院成都山地灾害与环境研究所编著，泥石流研究与防治[M]．四川科学技术出版社，1989，108-134．
[8] 李德基，1950-1989年四川发生的泥石流灾害[M]．四川抗灾经验——献给国际减轻自然灾害十年，四川人民出版社，1991，447-457．
[9] 罗元华等，中国山地灾害灾情评估[J]．中国减灾，1994，4(2)，18—25．
[10] 沈寿长等，中国铁路沿线泥石流[A]．泥石流及洪水灾害防御国际学术讨论会论文集(A卷)，1991，1-12．
[11] 钟敦伦等，金沙江下游四川片泥石流[A]．普查报告，1991，22-28．
[12] 刘希林，泥石流动力作用及其地貌标志[D]．[硕士生学位论文]，成都地理研究所，1986．
[13] Hakuno M. and Uchida Y., Application of the Distinct Element Method to the numerical analysis of debris flows [M]. Structural Eng. /Earthquake Eng, 1991, 8(2), 5-85, Proc, Japan Society of civil Engineers, 1991.
[14] 陈春光，姚令侃，禹华谦．泥石流与水流场交汇耦合分析的MAC法[J]．山地学报，2001(2)，185-188．
[15] Hardy J., Pomeau Y., de Pazzis O. , Time evolution of a twodimensional model system[J]. Journal of Mathematics Physical, 1973(14), 1746-1759.
[16] Frisch U., Hasslacher B., Pomeau Y., lattice-gas automata for the Navier-Stokes equation [J]. Physical Review, 1986 (56), 1505-1508.
[17] d' humieres, Lallemand P., Frisch U., Lattice gas methods for 3D hydrodynamics [J]. Europhys Letter, 1986(2), 291-297.
[18] Higuera F. J., Succi S., Simulating the flow around a circular cylinder with a lattice Boltzmann equation [J]. Europhys Letter, 1989 (8), 517-521.
[19] Qian Y. H., Lattice gas and lattice kinetic theory applied to the Navier-Stokes equations[D]. PHD thesis, Universite Puerrre Marie Curie, Paris, 1990.
[20] Chen S., Chen H. D. Martinez D., Matthaeus W. Lattice Boltzmann model for simulation of magnetohydrodynamics [J]. Physical Review Letters, 1991(67), 3776-3779.
[21] Chen H., Chen S., Matthaeus W. H., Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method[J], Physical Review A, 1992(45), 5339-5342.
[22] Qian Y. H, d'Humieres D., Lallemand P., Lattice BGK models for Navier-Stokes equation[J], Europhys Letter, 1992 (17), 479-484.
[23] Bhatnagar P. L, Gross E. P., Krook M., A Method for Collision Processes in Gases (1): Small Amplitude Processes in Charged and Neutral One-Component Systems[J]. Physical Review, 1954(94), 511-525.
[24] Higuera F. J., Succi S., Benzi R., Lattice gas dynamics with enhanced collisions[J]. Europhys Letter, 1989(9), 345-349.
[25] 李元香，格子气流体动力学的九点矩形模型[J]．武汉大学学报(并行计算专刊)，1991，22—32．
[26] Francesca N. and Sauro S., The lattice Boltzmann Equation on Irregular Lattices[J]. Journal Statistical Physics, 1992, 68(3/4): 401-407.
[27] 阎广武，胡守信，施卫平，守恒方程的差分型格子气方法[J]．计算物理，1997，14(2)，190—194．
[28] 阎广武，胡守信，施卫平，Euler 方程的双分布函数格子 Boltzmann Godunov方法[J]．计算物理，1998，15(2)，193—198．
[29] Alexander F. J., Chen H., Chen S. and Doolen GD., Lattice Boltzmann Model for Compressible fluids [J]. Physical Review A, 1992, 46(4), 1967-1970.
[30] 施卫平，胡守信，阎广武，计算可压缩流体流动的LB多速度模型[J]．吉林大学自然科学学报，1996，5(2)，7-12．
[31] Swift Michael R., Osborn W. R. and Yeomans JM., Lattice Boltzmann Model Simulation of Nonideal Fluids [J]. Physical Review letters, 1995(75), 830-833.
[32] Andrew K., Gunstensen H. and Daniel R., Lattice Boltzmann model of immiscible fluids [J]. Physical Review A, 1991(43), 4320-4327.
[33] Flekφy E. G., Lattice Bhatangar-Gross-Krook model for miscible fluids [J]. Physical Review E, 1993(47), 4247-4257.
[34] Richard H., Daniel H. and. Rothman F., Lattice-Gas and LatticeBoltzmann Models of Miscible Fluids[J]. Journal of Statistical Physics, 1992, 68 (3/4), 409-429.
[35] Alexander F. J., Chen S. and Sterling J. D., Lattice Boltzmann thermohydrodynamics[J]. Physical Review E, 1993, 47(4), 2249-2252.
[36] 盛武，李元香，康力山，陈炬桦，阮剑，热动力学格子Boltzmann模型[J]．计算物理，1998，15(4)，439-444．
[37] Yan Guangwu, Chen Yaosong and Hu Shouxin. Simple Lattice Boltzmann model for simulating flows with shock waves [J]. Physical Review E, 1999, 59(1), 9454-459.,
[38] Higuera F. J., Succi S. and Benzi R., Lattice Gas Dynamics With Enhanced Collisions[J], Europhys Letter, 1989, 9 (4), 345-349.
[39] 胡厚田等．高速远程滑坡流体动力学理论的研究[M]．西南交通大学出版社，2003．
[40] Chen H., Chen S., Matthaeus W. H., Recovery of the Navier-Stohes Equation Using a Lattice-gas Boltzmann Method[J]. Physical Review A, 1992(45), 5339-5342
[41] 俞慧丹，赵凯华．模拟可压缩流体的格子Boltzmann模型[J]．物理学报．1999，48(8)，1470-1476
[42] 施卫平，胡守信，阎广武．用改进的格子Boltzmann方法模拟浅水长波问题[J]．计算物理．1997，14(4／5)，663-665．
[43] 徐辉，刘贵苏等．流体动力学的格子Boltzmann方法及其具体实现[J]．燃烧科学与技术，1996，2(4)，406-410．
[44] 阎广武，邵显，胡守信．用格子Boltzmann方法研究波及其粘性实验[J]．吉林大学自然科学学报，1996(4)，23-27．
[45] 吴望一，流体力学(上册)[M]．北京大学出版社，1982．
[46] 潘文全主编，流体力学基础[M]．机械工业出版社，1980．
[47] 吴大猷，热力学，气体运动及统计力学[M]．科学出版社，1987．
[48] 黄祖洽，丁鄂江，输运理论[M]．科学出版社，1987．
[49] Wolfram S., Statistical mechanics of cellular automata[J]. Review Model Physics, 1983(55), 601-644.
[50] Wolfram S., Theory and applications of cellular automata[M]. World Scientific Publishing, Co, PTE. LTD, 1986.
[51] Hardy J., de Pazzis O., Pomeay Y., Molecular dynamics of a classical lattice gas transport properties and time correlation functions [J]. Physical Review A, 1976(13), 1949-1961.
[52] Frisch U., d' humieres D., Hasslacher B. lattice gas hydrodynamics in two and three dimensions [J]. Complex System, 1987(1), 649-707.
[53] Benzi R., Succi S. and Vergassola M., The Lattice Boltzmann Equation: theory and applications [J]. Physics Reports, 1992, 222(3), 145-197.
[54] Landau L. D., Lifshitz E. M. Statistical Physics[M]. Pergamon, 1978.
[55] d' humieres D., Lallemand P. Numerical Simulations of hydrodynamics with lattice gas automata in two dimensions[J]. Complex System, 1987(1), 599-632.
[56] Prigogine I．，Nicolis G．著，罗久里，陈奎宁译，探索复杂性[M]，四川教育出版社，1984．
[57] 李茹生，非平衡态热力学和耗散结构[M]，清华大学出版社，1986．
[58] 沈小峰、胡岗，姜璐，耗散结构论[M]，上海人民出版社，1987。
[59] Henon M., Complex System, Isometric Collision Rules for the FourDimensional FCHC Lattice Gas[J]. Complex Systems, 1987(1), 632-672.
[60] Frisch U., Rivet J. P., Gaz surreseau pour hydrodynamique formule de Green-Kubo[M], Compute Rend. Academe Science(Ⅱ), Paris, 1986(303), 1065-1068.
[61] Frisch U, Lattice Gas Method: theory and applications[J]. Physics D, 1991, 222(47), 231-239.
[62] Henon M., Implementation of the FCHC Lattice Gas Model on the Connection Machine[A]. Presented at the NATO Advanced Research Workshop on Lattice Gas Automata: theory, Implementating and Simulations, Nice, June, 25-28, 1991, Journal Statistical Physics 1992 (68), 353-359.
[63] Rothman D. H., Negative-Viscosity lattice gases[J]. Journal Statistical Physics, 1989(56), 517-524.
[64] Clavin P., Lallemand P., Pomeau Y., Searby G., Simulation of free Boundaries in flow systems by Lattice-gas models[J]. Journal Fluid Mechanics, 1988(188), 437-464.
[65] Rothman D. H., Zaleski S., Spinodal decomposition in a lattice-gas automaton [J], Journal Physics France, 1989(50), 2161-2174.
[66] Liyuanxiang, Kanglishan, A new class of Lattice gas methods[J]. Neural Parallel and Scientific Computations, 1993(1), 43-58.
[67] 聂思翔，圆管内通过圆孔板流动的格子气模拟[J]，武汉大学学报(并行计算专刊)，1991，33—38。
[68] Rothman D. H,, Kelller J. M., Immiscible cellular automaton fluids [J]. Journal Statistical Physics, 1988(52), 1119-1127.
[69] Gunstensen A. K., Rothman D. H., A Lattice-gas model for three immiscible fluids[J]. Physica D, 1991(47), 47-52.
[70] Gunstensen A. K., Rothman D. H., A Galilean-invariant immiscible Lattice gas[J]. Physica, 1991(47), 53-63.
[71] 李元香，Benard花纹的格子气模拟[J]，武汉大学学报(并行计算专刊)，1991，1-7．
[72] Chen H., Matthaeus W. H., Klein L. W., Theory of multicolor lattice gas: A cellular automaton Poisson solver [J]. Journal compute Physics, 1990(88), 433-466.
[73] Frish U., Hasslacher B., Pomeau Y., Lattice-gas Automata for the Navier-Stokes Equation [J]. Physics Review Letters, 1986(56), 1505-1508.
[74] Shiyi Chen, Gary Dand Doolen, Lattice Boltzmann Method For Fluid Flows[J]. Annual Reviews Fluid Mechanics, 1998(30), 329-364.
[75] Higuera FJ and Jimenez J, Boltzmann approach to lattice gas simulations [J] Europhys Letters, 1998(9), 663-668.
[76] 阎广武，用于流体动力学的Lattice Boltzmann方程[D]：[博士论文]．北京大学，1994．
[77] Hou S., Lattice Boltzmann method for incompressible viscous flow [D]. Phd thesis, Kansas State University, Manhattan Kansas, 1995.
[78] Tan MI, Qian YH, Goldhirsach I, Orszag SA, Lattice-BGK Approach to simulating Granular Flows[J]. Journal of Statistical Physics, 1995(81), No 1/2, 87-103.
[79] Hou S, Zon Q, Chen S, Doolen G, Cogley AC. Simulation of cavity flow by the lattice Boltzmann method[J]. Journal of compute Physics, 1995(118), 329-347.
[80] Miller W, Flow in the driven cavity calculated by the lattice Boltzmann method[J]. Physics Review E, 1995(51), 3659-3669.
[81] Grunau D, Chen S, Eggert K A, Lattice Boltzmann model for multiphase fluid flows[J]. Physics Fluid A, 1993 (5), 2557-2562.
[82] 赵继安，循环矩阵与矩阵对角化[J]．数学通报，1994(4)，41-42．
[83] Frisch U, Lattice Gas Methods: Theory, Applications and Hardware[J]. Physics D, 1991 (47), 198-203.
[84] 周雪漪，《计算水力学》[M]．清华大学出版社，1995年， 15-65．
[85] 蒋忠信，姚令侃，艾南山，崔之久著，铁路泥石流非线性燕余防治新技术[M]，四川科学技术出版社，1999，149—151．
[86] Fletcher CA, Burgers Equation A model for all reasons [D]. Proceeding Of the 1981 Conference on the Numerical Solution of PDE, Melbourne University, Australia, 1981.
[87] Evans DJ, Sahimi MS, The numerical solution of Burgers equation by the alternating group explicit age method[J]. International Journal Computer Mathematics, 1989(29), 39-64.
[88] 邹秀芬，对流扩散方程的格点模型[J]．计算物理，1996，13(3)，310-314．
[89] 韩庆书，龚霄雁，用特征型Galerkin方法求解Burgers方程[J]．水动力学研究与进展，1988，2(3)，101-113．
[90] 阎广武， 胡守信，施卫平，用于模拟弱可压缩Navier-Stokes方程的格子气模型[J]．吉林大学自然科学学报，1997，21(1)，1-6．
[91] Vano K, Daido A, Fundamental study on mudflow[D]. Bull Disaster Preview Research Institute, Kyoto University, Japan, 1965(Part 2), 69-83.
[92] AM．约翰逊著，张之立，李兴才译，地质学中的物理过程[M]．北京科学出版社，1991．
[93] Schowalter W R, Mechanics of non-Newtonian fluids [M]. Oxford Pergamon Press, 1978.
[94] 范椿，一维定常泥石流的数学模型[J]．力学与实践进展，1994，16(1)，50-52．
[95] Takahashi T. Mechanical characteristics of debris flow[J]. Journal of the Hydraulics Division, 1978(104), 1153-1169.
[96] Takahashi T. Debris flow on prismatic open channel[J]. Journal of the Hydraulics Division, 1980, 106(HY3), 381-396.
[97] then CL, Generalized Yiscoplastic Modeling of Debris Flow[J]. Journal of Hydraulic Engineering, 1988, 114(3), 237-258.
[98] Chen eL, General Solutions for Yiscoplastic Debris Flow[J]. Journal of Hydraulic Engineering, 1988, 114(3), 259-282.
[99] Keefer DK, et al. Real-time landslide warning during heavy rainfall[J]. Science, 1987, 13(238), 921-925.
[100] Iverson RM, The physics of debris flow[J]. Reviews of eophysics, 1997, 35 (3), 245-296.
[101] O' Brien JS, Julien PY and Fullerton WT, Tow dimensional water flood and mudflow simulation[J]. Journal of Hydraulic Engineering, 1993, 119(2), 244-261.
[102] Fan Chun范椿，泥石流及其运动方程[D]．Proceedings of The Sixth Asian Congress of Fluid Mechanics Singapor，1995，1179-1182．
[103] MacArthur RC，Hamilton D，Generalized Methodology for Simulating Mudflows[M]．第2届全国泥石流学术会议论文集，北京科学出版社，1986
[104] 田连权，吴积善，康志成等．泥石流侵蚀搬运与堆积[M]，成都地图出版社，1993．
[105] 王光谦，刘大有，费祥俊，泥石流的两相流模型和基本方程[D]．中国博士后论文集，230-239．
[106] 王光谦，倪晋仁，泥石流动力学基本方程[J]．科学通报，1991，39(18)，1700-1704．
[107] 沈寿长．泥石流应力本构关系[J]．水利学报．1998(12)，16-21．
[108] 吴积善，田连权，康志成等．泥石流及其综合治理[M]．科学出版社，1993．
[109] 章书成，陈英燕，袁晓凤，叶明富，粘性泥石流一维运动数学模型[J]．自然灾害学报，1996，5(4)，68-76．
[110] 崔之久，泥石流沉积与环境[M]．北京海洋出版社，1996．
[111] 田连权，吴积善，康志成等，泥石流侵蚀搬运与堆积[M]．成都地图出版社，1993，96—118．
[112] 刘希林，唐川．泥石流危险性评价[M]。北京科学出版社，1995．
[113] YAZAWA A, MIZUYAMA T, Computer simulation of debris flow depositional processes[M]. Erosion and Sedimentation in Pacific Rim (Proceeedings of the Corvallis Symposium, August, 1987), Iahs Publ, No165, 179-190.
[114] 王光谦，邵颂东，费翔俊．泥石流模拟：Ⅰ—模型[J]．泥沙研究，1998(9)，7-13．
[115] 王光谦，邵颂东，费翔俊．泥石流模拟：Ⅱ—理论[J]．泥沙研究，1998(9)，18-22．
[116] 王光谦，邵颂东，费翔俊．泥石流模拟：Ⅲ—应用[J]．泥沙研究，1998(9)，23-25．
[117] 倪晋仁，廖廉，曲轶众等．阵性泥石流运动与堆积的欧拉—拉格郎日模型——Ⅰ理论[J]．自然灾害学报2000，9(3)，8-14．
[118] 廖谦，倪晋仁，曲轶众等．阵性泥石流运动与堆积的欧拉—拉格郎日模型——Ⅱ应用[J]．自然灾害学报，2000，9(4)，15-18．
[119] 唐川，刘希林．泥石流动力堆积模拟和危险范围预测模型[J]．水土保持学报，1993，5(3)，37-40．
[120] 王裕宜．山区泥石流防治中堆积坡度预测模式的试验研究[J]．中国地质灾害与防治学报，1995，6(4)，58-67．
[121] 王裕宜，邹仁元等．泥石流堆积坡度预测模式的研究[A]究海峡两岸山地灾害与环境保育研究(第一卷)[M]．成都，四川省科技出版，1998．149-154．
[122] 刘学，王兴奎，王光谦．GIS与二维泥石流数学模型集成系统研究[J]．中国图形图形学报，1998，3(12)，1037-1040．
[123] 罗元华，陈崇希，武强．云南省东川市深沟泥石流堆积动态模拟及减灾效益评估[J]．地质学报，2001，75(1)，138-143．
[124] 周雪漪．《计算水力学》[M]．清华大学出版社，343-346．
[125] Chunguang Chen, LingKan Yao and Qin Wang. Numerical Simulation On The Confluence of Debris Flow And Main Channel By the MAC Method[J], Forecasting and Mitigation of Water-related Disaters, 2001, 16(21), 352-358.
[126] 吴积善，康志成，田连权，章书成主编．云南蒋家够泥石流观测研究[M]．科学出版社，1990年2月第一版．
[127] 李元香，陈炬桦，黄樟灿．LB方法的一个简单多速模型[J]．计算物理，1995， 12(4)，547-553．
[128] 王裕宜，泥石流浆体流变特性[J]．泥沙研究，1982(2)，75—78．
[2] 田连权，张信宝，吴积善．试论泥石流的形成过程[M]．泥石流文集(1)，科技文献出版社重庆分社，1981，54-59．
[3] 池谷浩，土石流的分类[J]．土木技术资料，1978，20(3)，323-325．
[4] 钱宁，王兆印．泥石流运动机理的初步探讨[J]．地理学报，1984，39(1)，33-43．
[5] 章书成，泥石流研究评述[J]．力学进展，1989，13(3)，365-374．
[6] 李德基主编，泥石流减灾理论与实践[M]．科学出版社，1997，31-32．
[7] 中国科学院成都山地灾害与环境研究所编著，泥石流研究与防治[M]．四川科学技术出版社，1989，108-134．
[8] 李德基，1950-1989年四川发生的泥石流灾害[M]．四川抗灾经验——献给国际减轻自然灾害十年，四川人民出版社，1991，447-457．
[9] 罗元华等，中国山地灾害灾情评估[J]．中国减灾，1994，4(2)，18—25．
[10] 沈寿长等，中国铁路沿线泥石流[A]．泥石流及洪水灾害防御国际学术讨论会论文集(A卷)，1991，1-12．
[11] 钟敦伦等，金沙江下游四川片泥石流[A]．普查报告，1991，22-28．
[12] 刘希林，泥石流动力作用及其地貌标志[D]．[硕士生学位论文]，成都地理研究所，1986．
[13] Hakuno M. and Uchida Y., Application of the Distinct Element Method to the numerical analysis of debris flows [M]. Structural Eng. /Earthquake Eng, 1991, 8(2), 5-85, Proc, Japan Society of civil Engineers, 1991.
[14] 陈春光，姚令侃，禹华谦．泥石流与水流场交汇耦合分析的MAC法[J]．山地学报，2001(2)，185-188．
[15] Hardy J., Pomeau Y., de Pazzis O. , Time evolution of a twodimensional model system[J]. Journal of Mathematics Physical, 1973(14), 1746-1759.
[16] Frisch U., Hasslacher B., Pomeau Y., lattice-gas automata for the Navier-Stokes equation [J]. Physical Review, 1986 (56), 1505-1508.
[17] d' humieres, Lallemand P., Frisch U., Lattice gas methods for 3D hydrodynamics [J]. Europhys Letter, 1986(2), 291-297.
[18] Higuera F. J., Succi S., Simulating the flow around a circular cylinder with a lattice Boltzmann equation [J]. Europhys Letter, 1989 (8), 517-521.
[19] Qian Y. H., Lattice gas and lattice kinetic theory applied to the Navier-Stokes equations[D]. PHD thesis, Universite Puerrre Marie Curie, Paris, 1990.
[20] Chen S., Chen H. D. Martinez D., Matthaeus W. Lattice Boltzmann model for simulation of magnetohydrodynamics [J]. Physical Review Letters, 1991(67), 3776-3779.
[21] Chen H., Chen S., Matthaeus W. H., Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method[J], Physical Review A, 1992(45), 5339-5342.
[22] Qian Y. H, d'Humieres D., Lallemand P., Lattice BGK models for Navier-Stokes equation[J], Europhys Letter, 1992 (17), 479-484.
[23] Bhatnagar P. L, Gross E. P., Krook M., A Method for Collision Processes in Gases (1): Small Amplitude Processes in Charged and Neutral One-Component Systems[J]. Physical Review, 1954(94), 511-525.
[24] Higuera F. J., Succi S., Benzi R., Lattice gas dynamics with enhanced collisions[J]. Europhys Letter, 1989(9), 345-349.
[25] 李元香，格子气流体动力学的九点矩形模型[J]．武汉大学学报(并行计算专刊)，1991，22—32．
[26] Francesca N. and Sauro S., The lattice Boltzmann Equation on Irregular Lattices[J]. Journal Statistical Physics, 1992, 68(3/4): 401-407.
[27] 阎广武，胡守信，施卫平，守恒方程的差分型格子气方法[J]．计算物理，1997，14(2)，190—194．
[28] 阎广武，胡守信，施卫平，Euler 方程的双分布函数格子 Boltzmann Godunov方法[J]．计算物理，1998，15(2)，193—198．
[29] Alexander F. J., Chen H., Chen S. and Doolen GD., Lattice Boltzmann Model for Compressible fluids [J]. Physical Review A, 1992, 46(4), 1967-1970.
[30] 施卫平，胡守信，阎广武，计算可压缩流体流动的LB多速度模型[J]．吉林大学自然科学学报，1996，5(2)，7-12．
[31] Swift Michael R., Osborn W. R. and Yeomans JM., Lattice Boltzmann Model Simulation of Nonideal Fluids [J]. Physical Review letters, 1995(75), 830-833.
[32] Andrew K., Gunstensen H. and Daniel R., Lattice Boltzmann model of immiscible fluids [J]. Physical Review A, 1991(43), 4320-4327.
[33] Flekφy E. G., Lattice Bhatangar-Gross-Krook model for miscible fluids [J]. Physical Review E, 1993(47), 4247-4257.
[34] Richard H., Daniel H. and. Rothman F., Lattice-Gas and LatticeBoltzmann Models of Miscible Fluids[J]. Journal of Statistical Physics, 1992, 68 (3/4), 409-429.
[35] Alexander F. J., Chen S. and Sterling J. D., Lattice Boltzmann thermohydrodynamics[J]. Physical Review E, 1993, 47(4), 2249-2252.
[36] 盛武，李元香，康力山，陈炬桦，阮剑，热动力学格子Boltzmann模型[J]．计算物理，1998，15(4)，439-444．
[37] Yan Guangwu, Chen Yaosong and Hu Shouxin. Simple Lattice Boltzmann model for simulating flows with shock waves [J]. Physical Review E, 1999, 59(1), 9454-459.,
[38] Higuera F. J., Succi S. and Benzi R., Lattice Gas Dynamics With Enhanced Collisions[J], Europhys Letter, 1989, 9 (4), 345-349.
[39] 胡厚田等．高速远程滑坡流体动力学理论的研究[M]．西南交通大学出版社，2003．
[40] Chen H., Chen S., Matthaeus W. H., Recovery of the Navier-Stohes Equation Using a Lattice-gas Boltzmann Method[J]. Physical Review A, 1992(45), 5339-5342
[41] 俞慧丹，赵凯华．模拟可压缩流体的格子Boltzmann模型[J]．物理学报．1999，48(8)，1470-1476
[42] 施卫平，胡守信，阎广武．用改进的格子Boltzmann方法模拟浅水长波问题[J]．计算物理．1997，14(4／5)，663-665．
[43] 徐辉，刘贵苏等．流体动力学的格子Boltzmann方法及其具体实现[J]．燃烧科学与技术，1996，2(4)，406-410．
[44] 阎广武，邵显，胡守信．用格子Boltzmann方法研究波及其粘性实验[J]．吉林大学自然科学学报，1996(4)，23-27．
[45] 吴望一，流体力学(上册)[M]．北京大学出版社，1982．
[46] 潘文全主编，流体力学基础[M]．机械工业出版社，1980．
[47] 吴大猷，热力学，气体运动及统计力学[M]．科学出版社，1987．
[48] 黄祖洽，丁鄂江，输运理论[M]．科学出版社，1987．
[49] Wolfram S., Statistical mechanics of cellular automata[J]. Review Model Physics, 1983(55), 601-644.
[50] Wolfram S., Theory and applications of cellular automata[M]. World Scientific Publishing, Co, PTE. LTD, 1986.
[51] Hardy J., de Pazzis O., Pomeay Y., Molecular dynamics of a classical lattice gas transport properties and time correlation functions [J]. Physical Review A, 1976(13), 1949-1961.
[52] Frisch U., d' humieres D., Hasslacher B. lattice gas hydrodynamics in two and three dimensions [J]. Complex System, 1987(1), 649-707.
[53] Benzi R., Succi S. and Vergassola M., The Lattice Boltzmann Equation: theory and applications [J]. Physics Reports, 1992, 222(3), 145-197.
[54] Landau L. D., Lifshitz E. M. Statistical Physics[M]. Pergamon, 1978.
[55] d' humieres D., Lallemand P. Numerical Simulations of hydrodynamics with lattice gas automata in two dimensions[J]. Complex System, 1987(1), 599-632.
[56] Prigogine I．，Nicolis G．著，罗久里，陈奎宁译，探索复杂性[M]，四川教育出版社，1984．
[57] 李茹生，非平衡态热力学和耗散结构[M]，清华大学出版社，1986．
[58] 沈小峰、胡岗，姜璐，耗散结构论[M]，上海人民出版社，1987。
[59] Henon M., Complex System, Isometric Collision Rules for the FourDimensional FCHC Lattice Gas[J]. Complex Systems, 1987(1), 632-672.
[60] Frisch U., Rivet J. P., Gaz surreseau pour hydrodynamique formule de Green-Kubo[M], Compute Rend. Academe Science(Ⅱ), Paris, 1986(303), 1065-1068.
[61] Frisch U, Lattice Gas Method: theory and applications[J]. Physics D, 1991, 222(47), 231-239.
[62] Henon M., Implementation of the FCHC Lattice Gas Model on the Connection Machine[A]. Presented at the NATO Advanced Research Workshop on Lattice Gas Automata: theory, Implementating and Simulations, Nice, June, 25-28, 1991, Journal Statistical Physics 1992 (68), 353-359.
[63] Rothman D. H., Negative-Viscosity lattice gases[J]. Journal Statistical Physics, 1989(56), 517-524.
[64] Clavin P., Lallemand P., Pomeau Y., Searby G., Simulation of free Boundaries in flow systems by Lattice-gas models[J]. Journal Fluid Mechanics, 1988(188), 437-464.
[65] Rothman D. H., Zaleski S., Spinodal decomposition in a lattice-gas automaton [J], Journal Physics France, 1989(50), 2161-2174.
[66] Liyuanxiang, Kanglishan, A new class of Lattice gas methods[J]. Neural Parallel and Scientific Computations, 1993(1), 43-58.
[67] 聂思翔，圆管内通过圆孔板流动的格子气模拟[J]，武汉大学学报(并行计算专刊)，1991，33—38。
[68] Rothman D. H,, Kelller J. M., Immiscible cellular automaton fluids [J]. Journal Statistical Physics, 1988(52), 1119-1127.
[69] Gunstensen A. K., Rothman D. H., A Lattice-gas model for three immiscible fluids[J]. Physica D, 1991(47), 47-52.
[70] Gunstensen A. K., Rothman D. H., A Galilean-invariant immiscible Lattice gas[J]. Physica, 1991(47), 53-63.
[71] 李元香，Benard花纹的格子气模拟[J]，武汉大学学报(并行计算专刊)，1991，1-7．
[72] Chen H., Matthaeus W. H., Klein L. W., Theory of multicolor lattice gas: A cellular automaton Poisson solver [J]. Journal compute Physics, 1990(88), 433-466.
[73] Frish U., Hasslacher B., Pomeau Y., Lattice-gas Automata for the Navier-Stokes Equation [J]. Physics Review Letters, 1986(56), 1505-1508.
[74] Shiyi Chen, Gary Dand Doolen, Lattice Boltzmann Method For Fluid Flows[J]. Annual Reviews Fluid Mechanics, 1998(30), 329-364.
[75] Higuera FJ and Jimenez J, Boltzmann approach to lattice gas simulations [J] Europhys Letters, 1998(9), 663-668.
[76] 阎广武，用于流体动力学的Lattice Boltzmann方程[D]：[博士论文]．北京大学，1994．
[77] Hou S., Lattice Boltzmann method for incompressible viscous flow [D]. Phd thesis, Kansas State University, Manhattan Kansas, 1995.
[78] Tan MI, Qian YH, Goldhirsach I, Orszag SA, Lattice-BGK Approach to simulating Granular Flows[J]. Journal of Statistical Physics, 1995(81), No 1/2, 87-103.
[79] Hou S, Zon Q, Chen S, Doolen G, Cogley AC. Simulation of cavity flow by the lattice Boltzmann method[J]. Journal of compute Physics, 1995(118), 329-347.
[80] Miller W, Flow in the driven cavity calculated by the lattice Boltzmann method[J]. Physics Review E, 1995(51), 3659-3669.
[81] Grunau D, Chen S, Eggert K A, Lattice Boltzmann model for multiphase fluid flows[J]. Physics Fluid A, 1993 (5), 2557-2562.
[82] 赵继安，循环矩阵与矩阵对角化[J]．数学通报，1994(4)，41-42．
[83] Frisch U, Lattice Gas Methods: Theory, Applications and Hardware[J]. Physics D, 1991 (47), 198-203.
[84] 周雪漪，《计算水力学》[M]．清华大学出版社，1995年， 15-65．
[85] 蒋忠信，姚令侃，艾南山，崔之久著，铁路泥石流非线性燕余防治新技术[M]，四川科学技术出版社，1999，149—151．
[86] Fletcher CA, Burgers Equation A model for all reasons [D]. Proceeding Of the 1981 Conference on the Numerical Solution of PDE, Melbourne University, Australia, 1981.
[87] Evans DJ, Sahimi MS, The numerical solution of Burgers equation by the alternating group explicit age method[J]. International Journal Computer Mathematics, 1989(29), 39-64.
[88] 邹秀芬，对流扩散方程的格点模型[J]．计算物理，1996，13(3)，310-314．
[89] 韩庆书，龚霄雁，用特征型Galerkin方法求解Burgers方程[J]．水动力学研究与进展，1988，2(3)，101-113．
[90] 阎广武， 胡守信，施卫平，用于模拟弱可压缩Navier-Stokes方程的格子气模型[J]．吉林大学自然科学学报，1997，21(1)，1-6．
[91] Vano K, Daido A, Fundamental study on mudflow[D]. Bull Disaster Preview Research Institute, Kyoto University, Japan, 1965(Part 2), 69-83.
[92] AM．约翰逊著，张之立，李兴才译，地质学中的物理过程[M]．北京科学出版社，1991．
[93] Schowalter W R, Mechanics of non-Newtonian fluids [M]. Oxford Pergamon Press, 1978.
[94] 范椿，一维定常泥石流的数学模型[J]．力学与实践进展，1994，16(1)，50-52．
[95] Takahashi T. Mechanical characteristics of debris flow[J]. Journal of the Hydraulics Division, 1978(104), 1153-1169.
[96] Takahashi T. Debris flow on prismatic open channel[J]. Journal of the Hydraulics Division, 1980, 106(HY3), 381-396.
[97] then CL, Generalized Yiscoplastic Modeling of Debris Flow[J]. Journal of Hydraulic Engineering, 1988, 114(3), 237-258.
[98] Chen eL, General Solutions for Yiscoplastic Debris Flow[J]. Journal of Hydraulic Engineering, 1988, 114(3), 259-282.
[99] Keefer DK, et al. Real-time landslide warning during heavy rainfall[J]. Science, 1987, 13(238), 921-925.
[100] Iverson RM, The physics of debris flow[J]. Reviews of eophysics, 1997, 35 (3), 245-296.
[101] O' Brien JS, Julien PY and Fullerton WT, Tow dimensional water flood and mudflow simulation[J]. Journal of Hydraulic Engineering, 1993, 119(2), 244-261.
[102] Fan Chun范椿，泥石流及其运动方程[D]．Proceedings of The Sixth Asian Congress of Fluid Mechanics Singapor，1995，1179-1182．
[103] MacArthur RC，Hamilton D，Generalized Methodology for Simulating Mudflows[M]．第2届全国泥石流学术会议论文集，北京科学出版社，1986
[104] 田连权，吴积善，康志成等．泥石流侵蚀搬运与堆积[M]，成都地图出版社，1993．
[105] 王光谦，刘大有，费祥俊，泥石流的两相流模型和基本方程[D]．中国博士后论文集，230-239．
[106] 王光谦，倪晋仁，泥石流动力学基本方程[J]．科学通报，1991，39(18)，1700-1704．
[107] 沈寿长．泥石流应力本构关系[J]．水利学报．1998(12)，16-21．
[108] 吴积善，田连权，康志成等．泥石流及其综合治理[M]．科学出版社，1993．
[109] 章书成，陈英燕，袁晓凤，叶明富，粘性泥石流一维运动数学模型[J]．自然灾害学报，1996，5(4)，68-76．
[110] 崔之久，泥石流沉积与环境[M]．北京海洋出版社，1996．
[111] 田连权，吴积善，康志成等，泥石流侵蚀搬运与堆积[M]．成都地图出版社，1993，96—118．
[112] 刘希林，唐川．泥石流危险性评价[M]。北京科学出版社，1995．
[113] YAZAWA A, MIZUYAMA T, Computer simulation of debris flow depositional processes[M]. Erosion and Sedimentation in Pacific Rim (Proceeedings of the Corvallis Symposium, August, 1987), Iahs Publ, No165, 179-190.
[114] 王光谦，邵颂东，费翔俊．泥石流模拟：Ⅰ—模型[J]．泥沙研究，1998(9)，7-13．
[115] 王光谦，邵颂东，费翔俊．泥石流模拟：Ⅱ—理论[J]．泥沙研究，1998(9)，18-22．
[116] 王光谦，邵颂东，费翔俊．泥石流模拟：Ⅲ—应用[J]．泥沙研究，1998(9)，23-25．
[117] 倪晋仁，廖廉，曲轶众等．阵性泥石流运动与堆积的欧拉—拉格郎日模型——Ⅰ理论[J]．自然灾害学报2000，9(3)，8-14．
[118] 廖谦，倪晋仁，曲轶众等．阵性泥石流运动与堆积的欧拉—拉格郎日模型——Ⅱ应用[J]．自然灾害学报，2000，9(4)，15-18．
[119] 唐川，刘希林．泥石流动力堆积模拟和危险范围预测模型[J]．水土保持学报，1993，5(3)，37-40．
[120] 王裕宜．山区泥石流防治中堆积坡度预测模式的试验研究[J]．中国地质灾害与防治学报，1995，6(4)，58-67．
[121] 王裕宜，邹仁元等．泥石流堆积坡度预测模式的研究[A]究海峡两岸山地灾害与环境保育研究(第一卷)[M]．成都，四川省科技出版，1998．149-154．
[122] 刘学，王兴奎，王光谦．GIS与二维泥石流数学模型集成系统研究[J]．中国图形图形学报，1998，3(12)，1037-1040．
[123] 罗元华，陈崇希，武强．云南省东川市深沟泥石流堆积动态模拟及减灾效益评估[J]．地质学报，2001，75(1)，138-143．
[124] 周雪漪．《计算水力学》[M]．清华大学出版社，343-346．
[125] Chunguang Chen, LingKan Yao and Qin Wang. Numerical Simulation On The Confluence of Debris Flow And Main Channel By the MAC Method[J], Forecasting and Mitigation of Water-related Disaters, 2001, 16(21), 352-358.
[126] 吴积善，康志成，田连权，章书成主编．云南蒋家够泥石流观测研究[M]．科学出版社，1990年2月第一版．
[127] 李元香，陈炬桦，黄樟灿．LB方法的一个简单多速模型[J]．计算物理，1995， 12(4)，547-553．
[128] 王裕宜，泥石流浆体流变特性[J]．泥沙研究，1982(2)，75—78．