基于FVM的滑坡运动三维动态仿真及应用
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摘要
滑坡是自然界中常见的灾害,分布广泛、发生频繁、危害性大。一旦失稳滑动,将严重威胁人民群众的生命财产和各种工程安全,造成重大损失。若能事先对滑坡的滑动特征及成灾范围有所估计和预测,对重大工程的布局以及减轻灾害均有重要意义。
滑坡失稳运动不是一个独立、纯粹的过程,而是与滑动前的整个滑坡系统紧密关联的。对滑坡运动过程仿真,必须基于滑坡系统科学。只有在详细研究滑坡形成条件、影响因素、形成机理和演化过程、稳定性分析和演化趋势的基础上,才能做出合理仿真和预测其灾害范围。本文在上述研究成果的基础上,基于滑坡运动学理论,建立滑坡运动模型及给出相应的控制方程,运用有限体积法,并参考CFD技术,采用VisualFortran编制专用计算程序,实现滑坡运动过程三维动态仿真。(1)介绍了两种主要滑坡运动模型—块体模型和Sassa模型,归纳现有常用的滑坡运动滑速、滑距计算方法。(2)简要阐述FVM的基本原理、网格结构、常用的离散格式、FVM的特点及其应用。(3)对滑坡体进行合理假设,给出滑坡运动控制方程,采用FVM进行离散,用VisualFortran编制计算程序,介绍了程序的基本功能和使用方法。(4)用兰州石峡口滑坡的实际滑动情况与计算仿真结果比较,得出仿真情况与实际基本符合,说明程序可行性。(5)预测积石峡水电站坝后Ⅰ号滑坡失稳运动情况和滑坡规模、淹没范围、滑坡坝、回水壅高等灾害情况。
Lanslides are common nature disasters with the characters of widely distributed, frequencely occurrences, large damages. They will seriously threaten peoples' lives and properties, will cause serious loses once sliding. For the engineering distribution and disasters' mitigation, it has very important significance to understand the characters of landslides' movements, to estimate the extensions in advance.
Landslides' movements are not absolute progresses, but tightly associated with landslides systems before sliding. So simulating the landslides' movements must be based on their system sciences. Reasonable simulation landslides' movements and predicting the disaster areas should base on the particular research of landslides' forming conditions, evolution mechanisms, stability analyse and the evolution trends of landslides. The dynamic movement model and control equations are put forward based on landslide kinematics theory. Finally the special calculation program is compiled to imitate landslides, movements adopting finite volume method and CFD technology. (1) Two existing landslide movement models including Block Model and Sassa Model are introduced and available common calculation methods are summarized. (2) The basic principles and grid structure of finite volume method (FVM) were briefly described and FVM's common-used discretization scheme and characteristics and application were introduced.(3) Based on reasonable hypothesis of landslide body, the control equations of landslide movement are given and landslide body is discretized by using FVM. A computation program has been made by Visual FORTRAN and its basic functions and using methods were introduced. (4) The sliding characteristics of Lanzhou Shixiakou landslide is emulated by using compiled special computer programs. Simulation results are compared with the actual sliding situation and found that the simulation results testify the rationality and practicability of the compiled special computer programs.(5)Study on No.1 downstream-Side landslide of Jishixia hydropower station, its movement conditions of landslide failure, landslide scale, inundated area, landslide dam, and run up height of backwater are predicted.
滑坡失稳运动不是一个独立、纯粹的过程,而是与滑动前的整个滑坡系统紧密关联的。对滑坡运动过程仿真,必须基于滑坡系统科学。只有在详细研究滑坡形成条件、影响因素、形成机理和演化过程、稳定性分析和演化趋势的基础上,才能做出合理仿真和预测其灾害范围。本文在上述研究成果的基础上,基于滑坡运动学理论,建立滑坡运动模型及给出相应的控制方程,运用有限体积法,并参考CFD技术,采用VisualFortran编制专用计算程序,实现滑坡运动过程三维动态仿真。(1)介绍了两种主要滑坡运动模型—块体模型和Sassa模型,归纳现有常用的滑坡运动滑速、滑距计算方法。(2)简要阐述FVM的基本原理、网格结构、常用的离散格式、FVM的特点及其应用。(3)对滑坡体进行合理假设,给出滑坡运动控制方程,采用FVM进行离散,用VisualFortran编制计算程序,介绍了程序的基本功能和使用方法。(4)用兰州石峡口滑坡的实际滑动情况与计算仿真结果比较,得出仿真情况与实际基本符合,说明程序可行性。(5)预测积石峡水电站坝后Ⅰ号滑坡失稳运动情况和滑坡规模、淹没范围、滑坡坝、回水壅高等灾害情况。
Lanslides are common nature disasters with the characters of widely distributed, frequencely occurrences, large damages. They will seriously threaten peoples' lives and properties, will cause serious loses once sliding. For the engineering distribution and disasters' mitigation, it has very important significance to understand the characters of landslides' movements, to estimate the extensions in advance.
Landslides' movements are not absolute progresses, but tightly associated with landslides systems before sliding. So simulating the landslides' movements must be based on their system sciences. Reasonable simulation landslides' movements and predicting the disaster areas should base on the particular research of landslides' forming conditions, evolution mechanisms, stability analyse and the evolution trends of landslides. The dynamic movement model and control equations are put forward based on landslide kinematics theory. Finally the special calculation program is compiled to imitate landslides, movements adopting finite volume method and CFD technology. (1) Two existing landslide movement models including Block Model and Sassa Model are introduced and available common calculation methods are summarized. (2) The basic principles and grid structure of finite volume method (FVM) were briefly described and FVM's common-used discretization scheme and characteristics and application were introduced.(3) Based on reasonable hypothesis of landslide body, the control equations of landslide movement are given and landslide body is discretized by using FVM. A computation program has been made by Visual FORTRAN and its basic functions and using methods were introduced. (4) The sliding characteristics of Lanzhou Shixiakou landslide is emulated by using compiled special computer programs. Simulation results are compared with the actual sliding situation and found that the simulation results testify the rationality and practicability of the compiled special computer programs.(5)Study on No.1 downstream-Side landslide of Jishixia hydropower station, its movement conditions of landslide failure, landslide scale, inundated area, landslide dam, and run up height of backwater are predicted.
引文
[1]孙园,李大心.滑坡监测的新方法—PMP测量方法[J].中国地质灾害与防治学报,2005,16(Supp):15-18
[2]文海家.基于GIS的滑坡灾变职能预测系统及应用研究[D].重庆:重庆大学,2004
[3]李天池.地震与滑坡的关系及地震滑坡预测探讨.滑坡文集(第二集)[M].北京:中国铁道出版社,1979:127-132
[4]H.Moriwaki,T.Inokuchi,T.Hattanji,et al.Failure processes in a full-scale landslide experiment using a rainfall simulator[J],landslides,2004,1:277-288
[5]Hirotaka Ochiai,Toshiaki Sammori,Yasuhiko Okada.Landslide Experiments on Artificial and Natural Slopes
[6]刘汉东.边坡位移矢量场与失稳定时预报试验研究[J].岩石力学与工程学报,1998,17(2):111-116
[7]刘涌江.大型高速岩质滑坡流体化理论研究[D].成都:西南交通大学,2002
[8]兰恒星,王苓涓,周成虎.地理信息系统支持下的滑坡灾害分析模型研究[J].工程地质学报,2002,10(4):421-427
[9]王恒星,周成虎,王苓涓,等.地理信息系统支持下的滑坡—水文耦合模型研究[J].岩石力学与工程学报,2003,22(8):1309-1314
[10]欧敏,张永兴,胡居义,等.基于Geo-CA和GIS的滑坡稳定性分析[J].中国地质灾害与防治学报,2004,15(4):1-6
[11]魏平新,汤连生,张建国,等.基于GIS的广东省滑坡灾害区划研究[J].水文地质工程地质,2005,4:6-9
[12]丛威青,潘懋,李铁锋,等.基于GIS的滑坡、泥石流灾害危险性区划关键问题[J].地学前言,2006,13(1):185-190
[13]白世彪,闾国年,盛业华.GIS技术在三峡库区滑坡灾害研究中的应用[J].2005,3:86-91
[14]乔建平,朱阿兴,陈永波,等.GIS与人工智能结合下的三维可视化滑坡危险度评价[J].中 国科学E辑技术科学,2003,33(Supp):79-84
[15]吴益平,唐辉明,姜玮.基于GIS的巴东新县城滑坡灾害风险系统[J].水文地质工程地质,2004,(Supp):117-121
[16]张建逃,许建瑞.基于GIS的滑坡信息管理和预测预报系统的设计[J].科技情报开发与经济,2005,15(12):226-227
[17]王俊岭,孙怀军.基于GIS的滑坡预测预报系统开发与研究[J].浙江水利科技,2005,3:6-8
[18]李先华,陈晓清,胡凯衡,等.GIS支持下的滑坡运动过程数字仿真[J].岩石力学与工程学报,2001,20(2):175-179
[19]Xie M,Esaki T,Zhou G Y,et al.Geographic Information systerm-based three-dimensional critical slope stability analysis and landslide hazard assessment[J].Journal of Geotechnical and Geoenvironmental Engnineering,2003,129(12):1109-1118
[20]田金华.滑坡可视化技术研究——滑坡体地面和滑动面3-D可视化模型[D].武汉:武汉理工大学,2004
[21]李先华,管群,相武年等.数字地形图上滑坡动态方向稳定系数的计算与滑坡滑动方向的确定[J].岩石力学与工程学报,1999,18(3):308-311
[22]李先华,陈晓清,李泳等.计算机的滑坡三维数字仿真[A].见:崔鹏编.海峡两岸山地灾害和环境保育学术研讨会文集[C],成都:四川省科学技术出版社,1998
[23]李先华,石火生,林珲等.GIS支持下降雨滑坡的启动机制研究与数字仿真[J].工程地质学报,2001,9(2):133-140
[24]Cundall P A.A Computer medel for simulating progressive large sacle movement in blocky systems [J],Proceeding of Symposium of Int.Soci.Rock Mesh.,Nacy,France,1971,1:2-8
[25]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用[M].沈阳:东北工学院出版社,1991
[26]程谦恭,彭建兵,胡广韬,等.高速岩质滑坡动力学[M].成都:西南交通大学出版社,1999
[27]程谦恭,胡厚田.剧冲式高速岩质滑坡全过程运动学数值模拟[J].西南交通大学学报,2000,35(1):18-22
[28]郑书彦.滑坡侵蚀及其动力学机制与定量评价研究[D].西安:西北农林科技大学,2002
[29]郑书彦,李占斌.公路滑坡侵蚀运动过程的仿真分析[J].长安大学学报(自然科学版),2007,27(2):21-25
[30]刘朋辉,魏迎奇,杨昭冬.贵州印江岩口滑坡过程的数值模拟分析[J].中国水利水电科学研究院学报,2007,5(2):115-120
[31]殷坤龙,姜清辉,汪洋.滑坡运动过程仿真分析[J].中国地质大学学报,2002,27(5):632-636
[32]Hazor Y H,Arziaa,Zaslavskyy,et al.Dynamic stability analysis of jointed rock slopes using the DDA method:King Herod's Palace,Masada,Isral[J].International Journal of Rock Mechanics and Minding Sciences,2004,41(5):813-832
[33]Sitar N,Maclaughlin M M,Doolin D M.Influence of kinematics on landslide mobility and failure mode[J].Journal of Geotechnical and Geoenvironmental Engineering,2005,131(6):716-728
[34]Qin S Q,Jiao J J,Wang S J.A nonlinear dynamical model of landslide evolution[J].Geomorphology,2002,43(1/2):77-85
[35]G.Inovire,D.D'Ambrosio,S.Di Gregorio.Applying genertic alogrithms for calibrating a hexagonal cellular automata model for the simulation of debris flow characterised by strong inertial effects[J].Geomorphology,2006,66:287-303
[36]Donato D'Ambrosio,Giulio Iovine,William Spataro,et al.A macroscopic collisional model for debris-flows simulation[J].Enviromental Modeling & Software,2007,22:1417-1436
[37]郑明新,马国正,王恭先,等.长晋高速公路顺层滑坡形成机理数值分析[J].华东交通大学学报,2007,24(5):1-4
[38]Vicente Medina,Marcel Harlimann,Allen Bateman.Application of FLATModel,a 2D finite volume code,to debris flows in the northeastern part of the Iberian Peninsula[J].landslides,2008,5:127-142
[39]McCormick B H,Defanti T A,Brown M D.Visualization in Scientific Computing[J].Computer Graphics.1987,21(6):12-15
[40]王延平.滑坡涌浪预测理论研究及计算模型开发[D].成都:成都理工大学,2005
[41]刘忠玉,马崇武,苗天德,等.高速滑坡远程预测的块体运动模型[J].岩石力学与工程学报,2000,19(6):742-746
[42]刘忠玉,方波.高速滑坡活动强度的动力模拟[J].郑州工业大学学报,2000,21(1):41-45
[43]马崇武,刘忠玉,苗天德,等.高速滑坡活动强度预测的一种新方法探讨[J].兰州大学学报(自然科学版),2001,37(1):93-96
[44]Miao T D,Liu Z.Y,Niu Y.H,et al.A sliding block model for the runout prediciton of high-speed landslides[J].Can.Geotech.J,2001,38:217-226
[45]王念秦,张倬元.黄土滑坡灾害研究fM].兰州:兰州大学出版社,2005:
[46]李未.有限体积模型及对涌潮形成动力机制的数值研究[D].南京:河海大学,2006
[47]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:
[48]李荣华.广义差分法及其应用[J].吉林大学自然科学学报,1995,1:14-21
[49]李荣华,祝丕琦.二阶椭圆偏微分方程的广义差分法(Ⅰ)-三边形网情形[J].高等学校计算数学学报,1982,18(2):140-152
[50]Ronghua L.Difference Methods for a Nonlinear Dirichlet Problem[J].SIAM J Numer Anal,1987,24(1):77-88
[51]苏丹,周飞.有限体积法仿真金属锻造过程及其关键技术[J].系统仿真学报,2003,15(4):534-537
[52]周飞,苏丹.有限体积法仿真金属塑性成形的基本理论[J].上海交通大学学报,2003,36(7):915-919
[53]黄克坚,包忠诩,周天瑞.有限体积数值模拟技术在型材变压变形规律研究中的运用[J].轻合金加工技术,2003,31(4):29-31
[54]张建立,李敏成,王长松.基于时空有点体积法的板坯凝固过程仿真[J].冶金设备,2007,162:1-5
[55]张谢东,吴秀恒.船舶水动力数值计算中的有限体积法[J].武汉造船,1998,4:4-7
[56]余斌.二维定常泥流的数值模拟[J].自然灾害学报,1995,4(4):96-99
[57]朱华君,宋松和.二维浅水波方程的非结构网格ENO型有限体积法[J].湖南师范大学自然科学版,2007,30(1):21-26
[58]褚克坚,华祖林,王惠民.二维浅水水流的一种新型三角形网格FVM计算格式[J].河海大学学报(自然科学版),2003,31(4):370-373
[59]陈祖华,赖冠文,王光谦,等.非规则网格下二维浅水流动的数值模拟[J].水科学进展,2002,13(6):657-664
[60]吕岁菊,王君超.有限体积法在土壤水分运动数值模拟中的应用[p].科技咨讯,2006,26(34):185-186
[61]张楚华,谷传纲,苗永淼.NS方程的非结构化网格方法及其差分格式[J].西安交通大学学报,1999,33(9):58-61
[62]杨勇,张福祥,曹丛咏,等.TVD有限体积法在二维超音速流计算中的应用[J].弹道学报, 1996,8(3):38-42
[63]韩华,程凌鹏,孙维志.基岩地下水流模型的摄动待定系数随机有限体积法及应用[J].工程勘察,2001,4:24-27
[64]刘高,邓建丽,梁昌玉.有限体积法在滑坡滑动过程模拟中的应用[J].地球科学进展,2007,22(11):1129-1133
[65]Barth T,Ohlberger M.Finite Volume Methods-Foundation and Analysis.in:Stein E,Thomas B,Hughes J R.Encyclopedia of Computational Mechanics.John Wiley & Sons.2004,
[66]Ferziger J H,Peric M.Computational Methods for Fluid Dynamics[M].Springer,2002
[67]Wood M K Brodlie,ViacANDGIS.Some Fundamental Considera2tions,Visualizationin Geograghical Infermation System,edited by Hi21aryM.Hearnshaw & DavidJ.Urwin.1994,3-8
[68]Visvalingam M.Visualizationnin GIS.Cartography and Vics.Visualiza2tionin Geographical Infermation System.Edited by HilaryM.Hearnshaw & DavidJ.Urwin.1994,18-25
[69]田金华,马俊生,池秀文.滑坡可视化与可视化软件IDL[J].西部探矿工程,2004,3:179-181
[70]李先华,林珲,龚建华,等.数字滑程与数字仿真应用研究[J].地球信息科学,2003,3:36-41
[2]文海家.基于GIS的滑坡灾变职能预测系统及应用研究[D].重庆:重庆大学,2004
[3]李天池.地震与滑坡的关系及地震滑坡预测探讨.滑坡文集(第二集)[M].北京:中国铁道出版社,1979:127-132
[4]H.Moriwaki,T.Inokuchi,T.Hattanji,et al.Failure processes in a full-scale landslide experiment using a rainfall simulator[J],landslides,2004,1:277-288
[5]Hirotaka Ochiai,Toshiaki Sammori,Yasuhiko Okada.Landslide Experiments on Artificial and Natural Slopes
[6]刘汉东.边坡位移矢量场与失稳定时预报试验研究[J].岩石力学与工程学报,1998,17(2):111-116
[7]刘涌江.大型高速岩质滑坡流体化理论研究[D].成都:西南交通大学,2002
[8]兰恒星,王苓涓,周成虎.地理信息系统支持下的滑坡灾害分析模型研究[J].工程地质学报,2002,10(4):421-427
[9]王恒星,周成虎,王苓涓,等.地理信息系统支持下的滑坡—水文耦合模型研究[J].岩石力学与工程学报,2003,22(8):1309-1314
[10]欧敏,张永兴,胡居义,等.基于Geo-CA和GIS的滑坡稳定性分析[J].中国地质灾害与防治学报,2004,15(4):1-6
[11]魏平新,汤连生,张建国,等.基于GIS的广东省滑坡灾害区划研究[J].水文地质工程地质,2005,4:6-9
[12]丛威青,潘懋,李铁锋,等.基于GIS的滑坡、泥石流灾害危险性区划关键问题[J].地学前言,2006,13(1):185-190
[13]白世彪,闾国年,盛业华.GIS技术在三峡库区滑坡灾害研究中的应用[J].2005,3:86-91
[14]乔建平,朱阿兴,陈永波,等.GIS与人工智能结合下的三维可视化滑坡危险度评价[J].中 国科学E辑技术科学,2003,33(Supp):79-84
[15]吴益平,唐辉明,姜玮.基于GIS的巴东新县城滑坡灾害风险系统[J].水文地质工程地质,2004,(Supp):117-121
[16]张建逃,许建瑞.基于GIS的滑坡信息管理和预测预报系统的设计[J].科技情报开发与经济,2005,15(12):226-227
[17]王俊岭,孙怀军.基于GIS的滑坡预测预报系统开发与研究[J].浙江水利科技,2005,3:6-8
[18]李先华,陈晓清,胡凯衡,等.GIS支持下的滑坡运动过程数字仿真[J].岩石力学与工程学报,2001,20(2):175-179
[19]Xie M,Esaki T,Zhou G Y,et al.Geographic Information systerm-based three-dimensional critical slope stability analysis and landslide hazard assessment[J].Journal of Geotechnical and Geoenvironmental Engnineering,2003,129(12):1109-1118
[20]田金华.滑坡可视化技术研究——滑坡体地面和滑动面3-D可视化模型[D].武汉:武汉理工大学,2004
[21]李先华,管群,相武年等.数字地形图上滑坡动态方向稳定系数的计算与滑坡滑动方向的确定[J].岩石力学与工程学报,1999,18(3):308-311
[22]李先华,陈晓清,李泳等.计算机的滑坡三维数字仿真[A].见:崔鹏编.海峡两岸山地灾害和环境保育学术研讨会文集[C],成都:四川省科学技术出版社,1998
[23]李先华,石火生,林珲等.GIS支持下降雨滑坡的启动机制研究与数字仿真[J].工程地质学报,2001,9(2):133-140
[24]Cundall P A.A Computer medel for simulating progressive large sacle movement in blocky systems [J],Proceeding of Symposium of Int.Soci.Rock Mesh.,Nacy,France,1971,1:2-8
[25]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用[M].沈阳:东北工学院出版社,1991
[26]程谦恭,彭建兵,胡广韬,等.高速岩质滑坡动力学[M].成都:西南交通大学出版社,1999
[27]程谦恭,胡厚田.剧冲式高速岩质滑坡全过程运动学数值模拟[J].西南交通大学学报,2000,35(1):18-22
[28]郑书彦.滑坡侵蚀及其动力学机制与定量评价研究[D].西安:西北农林科技大学,2002
[29]郑书彦,李占斌.公路滑坡侵蚀运动过程的仿真分析[J].长安大学学报(自然科学版),2007,27(2):21-25
[30]刘朋辉,魏迎奇,杨昭冬.贵州印江岩口滑坡过程的数值模拟分析[J].中国水利水电科学研究院学报,2007,5(2):115-120
[31]殷坤龙,姜清辉,汪洋.滑坡运动过程仿真分析[J].中国地质大学学报,2002,27(5):632-636
[32]Hazor Y H,Arziaa,Zaslavskyy,et al.Dynamic stability analysis of jointed rock slopes using the DDA method:King Herod's Palace,Masada,Isral[J].International Journal of Rock Mechanics and Minding Sciences,2004,41(5):813-832
[33]Sitar N,Maclaughlin M M,Doolin D M.Influence of kinematics on landslide mobility and failure mode[J].Journal of Geotechnical and Geoenvironmental Engineering,2005,131(6):716-728
[34]Qin S Q,Jiao J J,Wang S J.A nonlinear dynamical model of landslide evolution[J].Geomorphology,2002,43(1/2):77-85
[35]G.Inovire,D.D'Ambrosio,S.Di Gregorio.Applying genertic alogrithms for calibrating a hexagonal cellular automata model for the simulation of debris flow characterised by strong inertial effects[J].Geomorphology,2006,66:287-303
[36]Donato D'Ambrosio,Giulio Iovine,William Spataro,et al.A macroscopic collisional model for debris-flows simulation[J].Enviromental Modeling & Software,2007,22:1417-1436
[37]郑明新,马国正,王恭先,等.长晋高速公路顺层滑坡形成机理数值分析[J].华东交通大学学报,2007,24(5):1-4
[38]Vicente Medina,Marcel Harlimann,Allen Bateman.Application of FLATModel,a 2D finite volume code,to debris flows in the northeastern part of the Iberian Peninsula[J].landslides,2008,5:127-142
[39]McCormick B H,Defanti T A,Brown M D.Visualization in Scientific Computing[J].Computer Graphics.1987,21(6):12-15
[40]王延平.滑坡涌浪预测理论研究及计算模型开发[D].成都:成都理工大学,2005
[41]刘忠玉,马崇武,苗天德,等.高速滑坡远程预测的块体运动模型[J].岩石力学与工程学报,2000,19(6):742-746
[42]刘忠玉,方波.高速滑坡活动强度的动力模拟[J].郑州工业大学学报,2000,21(1):41-45
[43]马崇武,刘忠玉,苗天德,等.高速滑坡活动强度预测的一种新方法探讨[J].兰州大学学报(自然科学版),2001,37(1):93-96
[44]Miao T D,Liu Z.Y,Niu Y.H,et al.A sliding block model for the runout prediciton of high-speed landslides[J].Can.Geotech.J,2001,38:217-226
[45]王念秦,张倬元.黄土滑坡灾害研究fM].兰州:兰州大学出版社,2005:
[46]李未.有限体积模型及对涌潮形成动力机制的数值研究[D].南京:河海大学,2006
[47]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社,2004:
[48]李荣华.广义差分法及其应用[J].吉林大学自然科学学报,1995,1:14-21
[49]李荣华,祝丕琦.二阶椭圆偏微分方程的广义差分法(Ⅰ)-三边形网情形[J].高等学校计算数学学报,1982,18(2):140-152
[50]Ronghua L.Difference Methods for a Nonlinear Dirichlet Problem[J].SIAM J Numer Anal,1987,24(1):77-88
[51]苏丹,周飞.有限体积法仿真金属锻造过程及其关键技术[J].系统仿真学报,2003,15(4):534-537
[52]周飞,苏丹.有限体积法仿真金属塑性成形的基本理论[J].上海交通大学学报,2003,36(7):915-919
[53]黄克坚,包忠诩,周天瑞.有限体积数值模拟技术在型材变压变形规律研究中的运用[J].轻合金加工技术,2003,31(4):29-31
[54]张建立,李敏成,王长松.基于时空有点体积法的板坯凝固过程仿真[J].冶金设备,2007,162:1-5
[55]张谢东,吴秀恒.船舶水动力数值计算中的有限体积法[J].武汉造船,1998,4:4-7
[56]余斌.二维定常泥流的数值模拟[J].自然灾害学报,1995,4(4):96-99
[57]朱华君,宋松和.二维浅水波方程的非结构网格ENO型有限体积法[J].湖南师范大学自然科学版,2007,30(1):21-26
[58]褚克坚,华祖林,王惠民.二维浅水水流的一种新型三角形网格FVM计算格式[J].河海大学学报(自然科学版),2003,31(4):370-373
[59]陈祖华,赖冠文,王光谦,等.非规则网格下二维浅水流动的数值模拟[J].水科学进展,2002,13(6):657-664
[60]吕岁菊,王君超.有限体积法在土壤水分运动数值模拟中的应用[p].科技咨讯,2006,26(34):185-186
[61]张楚华,谷传纲,苗永淼.NS方程的非结构化网格方法及其差分格式[J].西安交通大学学报,1999,33(9):58-61
[62]杨勇,张福祥,曹丛咏,等.TVD有限体积法在二维超音速流计算中的应用[J].弹道学报, 1996,8(3):38-42
[63]韩华,程凌鹏,孙维志.基岩地下水流模型的摄动待定系数随机有限体积法及应用[J].工程勘察,2001,4:24-27
[64]刘高,邓建丽,梁昌玉.有限体积法在滑坡滑动过程模拟中的应用[J].地球科学进展,2007,22(11):1129-1133
[65]Barth T,Ohlberger M.Finite Volume Methods-Foundation and Analysis.in:Stein E,Thomas B,Hughes J R.Encyclopedia of Computational Mechanics.John Wiley & Sons.2004,
[66]Ferziger J H,Peric M.Computational Methods for Fluid Dynamics[M].Springer,2002
[67]Wood M K Brodlie,ViacANDGIS.Some Fundamental Considera2tions,Visualizationin Geograghical Infermation System,edited by Hi21aryM.Hearnshaw & DavidJ.Urwin.1994,3-8
[68]Visvalingam M.Visualizationnin GIS.Cartography and Vics.Visualiza2tionin Geographical Infermation System.Edited by HilaryM.Hearnshaw & DavidJ.Urwin.1994,18-25
[69]田金华,马俊生,池秀文.滑坡可视化与可视化软件IDL[J].西部探矿工程,2004,3:179-181
[70]李先华,林珲,龚建华,等.数字滑程与数字仿真应用研究[J].地球信息科学,2003,3:36-41