地下水流有限差分计算可视化系统的研究与开发
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摘要
有限差分法是一种重要的数值计算方法。该方法的应用使水文地质学计算得到了迅速发展。当前科学计算可视化是水文地质计算领域的一个重要研究方向。本文采用有限差分法,并结合可视化技术,解决水文地质计算领域的部分渗流问题,对实际工作有重要意义。
实际的水文地质条件往往是比较复杂的,用解析法求解很困难,数值法为研究这类问题开辟了新的途径。它以地下水渗流理论为基础,从整个计算区域的水量平衡或质量守恒出发,建立反映整个计算区域地下水运动状况的数学模型。有限差分法是数值模拟最早采用的方法,该方法把控制方程中的导数用网格节点上的函数值的差商代替,边界条件、初始条件也相应地做类似代替,从而建立以网格节点上的值为未知数的代数方程组。其数学概念直观,表达简单,是发展比较成熟的数值方法。
本文以有限差分法为基础,采用面向对象的思想,以Visual Basic6.0为开发平台,研发了关于地下水流计算的可视化系统。系统从功能上被划分为前处理、有限差分计算、后处理三大模块。前处理阶段主要完成了矩形网格剖分和不规则三角网格剖分。不规则三角网的生成采用逐点插入法。计算阶段结合实际水文地质条件,选择适当的数学模型,以有限差分法为基础,完成一维、二维承压稳定流及非稳定流计算的分析、设计和实现。后处理阶段,采用ActiveX Automation技术,在VB下与Surfer接口进行嵌入式编程,快速高效地绘制出等水头线图及立体表面图。采用OpenGL技术,绘制出非稳定流的水头变化曲线。
本系统以承压含水层二维非稳定流为工程实例对系统主要功能进行测试,验证了系统在计算地下水流水头分布时具有一定的可行性。
FDM(Finite Difference Method) is one of the important numeric calculation methods used in Groundwater Gynamics.The application of FDM has advanced rapidly Groundwater Gynamics. Visualization in Scientific Computing is a important studying direction in the fields of calculation in Groundwater Gynamics. The calculation of FDM need the support of Visualization in Scientific Computing, which makes for the development of Groundwater Gynamics.
Actual hydrological and geological conditions are often more complex, using theanalytic method is very difficult,.numerical method to study these issues has opened up new ways. It based on groundwater percolation theory and water balance or quality conservation builds mathematical model which can reflect the whole regional groundwater movement. Being the earliest numerical simulation methods, derivatives of control equation are replaced with differece quatient of grid node function ,correspondingly, boundary and initial conditions dealed in similar, by which FDM set up equation set ,value of grid nodes unknown.With intuitive mathematical concepts, simple expression fdm is one of mature numerical methods.The paper system uses object-oriented thinking, based on the finite difference method, Visual Basic6.0 platform for the development, research and development on the basis of groundwater flow visualization system.From the functions of the system is divided into pre-processing, finite difference, post-processing module. The pre-processing stages can finish rectangular grid and the irregular triangular grid. TIN generated by the insertion point by point. In calculation stage,the system according to hydrological and geological conditions, selecting the appropriate mathematical model, based on the finite difference method, can finish one-dimensional, two-dimensional pressure steady flow and non-steady flow of the analysis, design and implementation.In post-processing phase, the system ,using ActiveX Automation technology, embedded Surfer in VB programming quickly ,efficiently plot coutour map. The system using OpenGL draw a non-steady flow curve.
The system selects confined aquifer two-dimensional non-steady flow as engineering examples to test main functions,which is feasible for calculating the distribution of water head.
实际的水文地质条件往往是比较复杂的,用解析法求解很困难,数值法为研究这类问题开辟了新的途径。它以地下水渗流理论为基础,从整个计算区域的水量平衡或质量守恒出发,建立反映整个计算区域地下水运动状况的数学模型。有限差分法是数值模拟最早采用的方法,该方法把控制方程中的导数用网格节点上的函数值的差商代替,边界条件、初始条件也相应地做类似代替,从而建立以网格节点上的值为未知数的代数方程组。其数学概念直观,表达简单,是发展比较成熟的数值方法。
本文以有限差分法为基础,采用面向对象的思想,以Visual Basic6.0为开发平台,研发了关于地下水流计算的可视化系统。系统从功能上被划分为前处理、有限差分计算、后处理三大模块。前处理阶段主要完成了矩形网格剖分和不规则三角网格剖分。不规则三角网的生成采用逐点插入法。计算阶段结合实际水文地质条件,选择适当的数学模型,以有限差分法为基础,完成一维、二维承压稳定流及非稳定流计算的分析、设计和实现。后处理阶段,采用ActiveX Automation技术,在VB下与Surfer接口进行嵌入式编程,快速高效地绘制出等水头线图及立体表面图。采用OpenGL技术,绘制出非稳定流的水头变化曲线。
本系统以承压含水层二维非稳定流为工程实例对系统主要功能进行测试,验证了系统在计算地下水流水头分布时具有一定的可行性。
FDM(Finite Difference Method) is one of the important numeric calculation methods used in Groundwater Gynamics.The application of FDM has advanced rapidly Groundwater Gynamics. Visualization in Scientific Computing is a important studying direction in the fields of calculation in Groundwater Gynamics. The calculation of FDM need the support of Visualization in Scientific Computing, which makes for the development of Groundwater Gynamics.
Actual hydrological and geological conditions are often more complex, using theanalytic method is very difficult,.numerical method to study these issues has opened up new ways. It based on groundwater percolation theory and water balance or quality conservation builds mathematical model which can reflect the whole regional groundwater movement. Being the earliest numerical simulation methods, derivatives of control equation are replaced with differece quatient of grid node function ,correspondingly, boundary and initial conditions dealed in similar, by which FDM set up equation set ,value of grid nodes unknown.With intuitive mathematical concepts, simple expression fdm is one of mature numerical methods.The paper system uses object-oriented thinking, based on the finite difference method, Visual Basic6.0 platform for the development, research and development on the basis of groundwater flow visualization system.From the functions of the system is divided into pre-processing, finite difference, post-processing module. The pre-processing stages can finish rectangular grid and the irregular triangular grid. TIN generated by the insertion point by point. In calculation stage,the system according to hydrological and geological conditions, selecting the appropriate mathematical model, based on the finite difference method, can finish one-dimensional, two-dimensional pressure steady flow and non-steady flow of the analysis, design and implementation.In post-processing phase, the system ,using ActiveX Automation technology, embedded Surfer in VB programming quickly ,efficiently plot coutour map. The system using OpenGL draw a non-steady flow curve.
The system selects confined aquifer two-dimensional non-steady flow as engineering examples to test main functions,which is feasible for calculating the distribution of water head.
引文
[1] 薛禹群,朱学愚.地下水动力学[M].北京:地质出版社,1986.1～2
[2] 王大纯,张人权.水文地质学基础[M].北京:地质出版社,1995.1～5
[3] 李俊亭,王愈吉.地下水动力学[M].北京:地质出版社,1987.1～3 179～191
[4] Wu Qiang, Yin Zhongmin, Wu Xun. Groundwater Study in the WeerselArea, Overijssel, the Netherlands[M].Beijing:Petroleum IndustrPress,2001.47～74.
[5] 魏林宏,束龙仓,郝振纯.地下水流数值模拟的研究现状和发展趋势[J].重庆大学学报,2000,10(23):50～53
[6] 陈崇希,唐仲华.地下水流动问题数值方法[M].北京:中国地质大学出版社,1990.1～2
[7] 孙峰根,王晓明.水文地质计算的数值方法[M].北京:中国矿业大学出版社,1995.1～2 18～26
[8] MEHLS,HILLC.Development and evaluation of a localgrid refinement method for block centered finite difference groundwater models using shared nodes J.Advances in Water Resources.2002 ,25:497~511.
[9] OLSTHOORN TN.A comparative reviewof analytic and finit difference models used at the Amsterdam Water Supply.Journal of Hydrology,1999 ,226:139~143.
[10] 石教英,蔡文立.科学计算可视化算法与系统[M].北京:科学出版社,1996.1～18
[11] 唐泽圣,孙延奎,邓俊辉.科学计算可视化理论与应用研究进展.清华大学学报[J],2001,41(45):200～202
[12] 戴会超,田斌.科学计算可视化仿真及其在水利行业中的应用[J].水力发电学报,2005,24(6):88～90
[13] 韩程辉,刘文生.地下水模拟系统(GMS)与矿井防治水[J].矿业安全与环保,2005,1(32):25～26
[14] 贺国平,张彤,赵月芬,周东.GMS 数值建模方法研究综述[J].地下水,2007,29(3):32～35
[15] 梁煦枫,王文科,曾永刚.GMS 在水文地质结构可视化方面的应用[J].东北水利水电,2006,9(24):64~66
[16] 马驰,石辉,卢玉东.MODFLOW 在西北地区地下水资源评价中的应用[J].干旱区资源与环境,2006.20(1):80～90
[17] 马平,张志修.MODFLOW 在山东文登抽水蓄能电站探洞涌水评价中的应用[J].工程勘察,2006,3:16
[18] Laura K. Lautz and Donald I. Siegel .Modeling surface and ground water mixing in the hyporheic zone using MODFLOW and MT3D[J].ARTICLE Advances in WaterResources,2006,29(11):1618～1633
[19] Richard B. Winston .MODFLOW-related freeware and shareware resources on the internet.Computers & Geosciences,1999,25( 4):377～382
[20] WINSTON R B. Upgrade to MODFLOW GUI:Addition of MOD PATH ,ZONEBDGT,and Additional MODFLOW Packages to theU. S. Geological Survey MODFLOW - 96 Graphical - User Interface.U S Geological Survey Open - File Report ,1999.
[21] 陈崇希,胡立堂,王旭升.地下水流模拟系统 PGMS(110 版)简介[J].水文地质工程质,2007,6:1～2
[22] ANDERSON M P,WOESSNER W W.Applied groundwater modeling:Simulation of flow and advective transport M.NewYork:Academic Press Inc,1992:145~152.
[23] 郝治福,康绍忠.地下水系统数值模拟的研究现状和发展趋势[J].水利水电科技进展,2006,26(1):77～78
[24] 陈练武.计算机地质制图概论[M].西安:西安地图出版社,2004.31～42
[25] 周知.三角剖分算法研究:[学位论文].哈尔滨:哈尔滨理工大学,2007
[26] 金世双.离散数据三角网格剖分研究与实现[J].上海海军大学学报,2005,26(3):86～88
[27] 朱东林.基于 Delaunay 三角剖分法在节理图上实现网格自动剖分[J].岩石力学与工程学报,2004,23(11):45~47
[28] Lee D T. and Schachter B J. Two Algorithms for Constructing a Delaunay Triangulation, Int. Computer and Information Sciences,1980,9(3)
[29] Watson D F. Computing the n2dimension Delaunay Tesselation with Application to Voronoi Polytopes.Computer Journal,1981(24):167～172
[30] McCaullaghM T. and RossC G. Delaunay Triangulation of a Random Data Set For Iirarithmic Mapping. The Cartographic Journal,1980(17):93～99
[31] 刘沂轩,熊彩霞,周保太.Surfer8.0 在地下水监测管理中的应用.能源技术与管理[J].2007,6:148～150
[32] 马占良,王振宇.Surfer 绘图及其在 VB 编程中的自动化控制[J].信息管理,2007,6:82～84
[33] 张莹,张胜业,昌彦君.Surfer Automation 技术在电法资料成图中的应用[J].工程地球物理学报,2005,2:50~52
[34] 徐士良,朱明方.软件应用技术基础[M].北京:清华大学出版社,2000.179～197
[35] 张海藩.软件工程导论[M].北京:清华大学出版社,2000.1～20
[36] 安杰尔.OpenGL 程序指南[M].北京:清华大学出版社,2005.1～20
[37] 李庆,巫影,胡大斌.利用 OpenGL 技术实现科学计算可视化[J].武汉理工大学学报,2002,24(3):37～39
[2] 王大纯,张人权.水文地质学基础[M].北京:地质出版社,1995.1～5
[3] 李俊亭,王愈吉.地下水动力学[M].北京:地质出版社,1987.1～3 179～191
[4] Wu Qiang, Yin Zhongmin, Wu Xun. Groundwater Study in the WeerselArea, Overijssel, the Netherlands[M].Beijing:Petroleum IndustrPress,2001.47～74.
[5] 魏林宏,束龙仓,郝振纯.地下水流数值模拟的研究现状和发展趋势[J].重庆大学学报,2000,10(23):50～53
[6] 陈崇希,唐仲华.地下水流动问题数值方法[M].北京:中国地质大学出版社,1990.1～2
[7] 孙峰根,王晓明.水文地质计算的数值方法[M].北京:中国矿业大学出版社,1995.1～2 18～26
[8] MEHLS,HILLC.Development and evaluation of a localgrid refinement method for block centered finite difference groundwater models using shared nodes J.Advances in Water Resources.2002 ,25:497~511.
[9] OLSTHOORN TN.A comparative reviewof analytic and finit difference models used at the Amsterdam Water Supply.Journal of Hydrology,1999 ,226:139~143.
[10] 石教英,蔡文立.科学计算可视化算法与系统[M].北京:科学出版社,1996.1～18
[11] 唐泽圣,孙延奎,邓俊辉.科学计算可视化理论与应用研究进展.清华大学学报[J],2001,41(45):200～202
[12] 戴会超,田斌.科学计算可视化仿真及其在水利行业中的应用[J].水力发电学报,2005,24(6):88～90
[13] 韩程辉,刘文生.地下水模拟系统(GMS)与矿井防治水[J].矿业安全与环保,2005,1(32):25～26
[14] 贺国平,张彤,赵月芬,周东.GMS 数值建模方法研究综述[J].地下水,2007,29(3):32～35
[15] 梁煦枫,王文科,曾永刚.GMS 在水文地质结构可视化方面的应用[J].东北水利水电,2006,9(24):64~66
[16] 马驰,石辉,卢玉东.MODFLOW 在西北地区地下水资源评价中的应用[J].干旱区资源与环境,2006.20(1):80～90
[17] 马平,张志修.MODFLOW 在山东文登抽水蓄能电站探洞涌水评价中的应用[J].工程勘察,2006,3:16
[18] Laura K. Lautz and Donald I. Siegel .Modeling surface and ground water mixing in the hyporheic zone using MODFLOW and MT3D[J].ARTICLE Advances in WaterResources,2006,29(11):1618～1633
[19] Richard B. Winston .MODFLOW-related freeware and shareware resources on the internet.Computers & Geosciences,1999,25( 4):377～382
[20] WINSTON R B. Upgrade to MODFLOW GUI:Addition of MOD PATH ,ZONEBDGT,and Additional MODFLOW Packages to theU. S. Geological Survey MODFLOW - 96 Graphical - User Interface.U S Geological Survey Open - File Report ,1999.
[21] 陈崇希,胡立堂,王旭升.地下水流模拟系统 PGMS(110 版)简介[J].水文地质工程质,2007,6:1～2
[22] ANDERSON M P,WOESSNER W W.Applied groundwater modeling:Simulation of flow and advective transport M.NewYork:Academic Press Inc,1992:145~152.
[23] 郝治福,康绍忠.地下水系统数值模拟的研究现状和发展趋势[J].水利水电科技进展,2006,26(1):77～78
[24] 陈练武.计算机地质制图概论[M].西安:西安地图出版社,2004.31～42
[25] 周知.三角剖分算法研究:[学位论文].哈尔滨:哈尔滨理工大学,2007
[26] 金世双.离散数据三角网格剖分研究与实现[J].上海海军大学学报,2005,26(3):86～88
[27] 朱东林.基于 Delaunay 三角剖分法在节理图上实现网格自动剖分[J].岩石力学与工程学报,2004,23(11):45~47
[28] Lee D T. and Schachter B J. Two Algorithms for Constructing a Delaunay Triangulation, Int. Computer and Information Sciences,1980,9(3)
[29] Watson D F. Computing the n2dimension Delaunay Tesselation with Application to Voronoi Polytopes.Computer Journal,1981(24):167～172
[30] McCaullaghM T. and RossC G. Delaunay Triangulation of a Random Data Set For Iirarithmic Mapping. The Cartographic Journal,1980(17):93～99
[31] 刘沂轩,熊彩霞,周保太.Surfer8.0 在地下水监测管理中的应用.能源技术与管理[J].2007,6:148～150
[32] 马占良,王振宇.Surfer 绘图及其在 VB 编程中的自动化控制[J].信息管理,2007,6:82～84
[33] 张莹,张胜业,昌彦君.Surfer Automation 技术在电法资料成图中的应用[J].工程地球物理学报,2005,2:50~52
[34] 徐士良,朱明方.软件应用技术基础[M].北京:清华大学出版社,2000.179～197
[35] 张海藩.软件工程导论[M].北京:清华大学出版社,2000.1～20
[36] 安杰尔.OpenGL 程序指南[M].北京:清华大学出版社,2005.1～20
[37] 李庆,巫影,胡大斌.利用 OpenGL 技术实现科学计算可视化[J].武汉理工大学学报,2002,24(3):37～39
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