基于格子Boltzmann方法的地下突水数值模拟
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摘要
巷道突水是指开采矿层时,在水压和矿压等因素综合作用下,底板含水层内的地下水突破矿层或含水层间的相对隔水层,沿断层、节理等结构面突然涌入矿井的现象。巷道突水是一种与工程和采矿活动有关的诱发性地质灾害,是工程地质问题。大量突水,不仅淹没巷道和井巷,还能导致塌方和围岩失稳,甚至造成人身伤亡、工程报废的灾难性结果。因此选择科学的方法,研究地下突水在巷道内的变化情况和运行规律,对于我们提高矿山生产安全,保障人员财产有重要的指导意义。
通过阅读大量的文献资料,了解了目前国内外学者在地下突水方面的研究的现状,发现学者在突水数值模拟方面所做的研究相对来说少一些,其中以东北大学和中国矿业大学为主,且采用有限元方法结合FLAC软件进行模拟,解决方法较为单一。所以本文选择在诸多领域已经有很好研究成果的格子Boltzmann来对地下突水情况进行研究。
首先研究了一个二维巷道的突水过程。通过介绍D2Q9模型来向大家介绍格子Boltzmann的方法原理。为了提高模拟的可靠性和精度,我们选择了Guo等人提出的针对类似于水一样的不可压缩流体的G2Q9模型。在进行边界处理的时候,根据不同的边界情况,我们选择了不同的解决方法。对于平直边界来说,我们选用了修正的反弹格式进行处理,对于那些不规则的边界来说,我们选用BFL进行曲面边界的处理。同时由于巷道结构的复杂,为了降低运算量,提高运算的效率,我们使用分块耦合的方法对巷道进行了相应的处理。最后通过一个实例模拟来验证我们的理论。
其次针对突水抢救的两种方式进行了数值模拟,提出堵式模拟和疏式模拟模型。对于堵式模拟,我们建立了相应的突水阻滞模型,使用BFL进行边界的处理。通过模拟挡水墙的完成情况,我们得到了不同时刻的巷道内的压力、速度、流向等结果,分析这些结果,我们可以比较清楚的看到这种方法对于巷道内压力,速度,水流方向的改变都有一定的作用,符合我们的预期情况。对于疏式模拟,我们建立了相应的抽放模型,并使用作用力的方式来模拟抽水机的原理,最后通过对比有压力和无压力下的两种状况,得到的各种压力图,速度图,流线图等结果满足了我们的期望值。
最后为了直观清楚的了解LBM方法在巷道突水方面的模拟作用,我们在前两章的基础上,我们选用D3Q15模型来对三维巷道的突水情况进行模拟。最后也通过一个实例模拟来验证了我们的理论。
如何简化处理复杂的巷道问题,如何选用合适的Boltzmann模型,如何进行网格边界的处理,如何提高程序的运行效率,如何得到满意的仿真结果,这些都是本文的研究重点。本文的研究对于矿山开发,综合治理,以及相关技术的研究提供了方法参考和研究依据。
?Tunnel water-inrush in tunnel is a phenomenon that means groundwater in the bottom aquifer breaks mine seam or relatively impermeable layer between aquifers along faults, joints and other structural plane inrush mine suddenly, under the combined effects of factors such as the water pressure and rock pressure, when the mine was exploited Tunnel water-inrush is a induced geological disasters which related with engineering and mining activities. It is engineering geological problems. Large inrush of water is not only flooded mine tunnel , but also can cause collapse and rock unstable, or even result in disastrous results like personal injury and construction scrapped. So it has important guiding significance in improve mine safety and guarantee officers and properties for us selecting scientific method to study the water-inrush changes and movement law in tunnel.
I understand the research status in water-inrush from domestic and foreign scholars after reading large amount of literatures. And find that there is a relatively small number scholar to study water-inrush simulation, in which Northeastern University and China University of Mining and Technology are stay on top. They simulate the water-inrush combined the finite element method and FLAC software, the solution is relatively homogeneous. So the paper adapts Lattice Boltzmann Method to simulate tunnel water-inrush, which has a lot of great research result in many fields.
We study a two-dimensional tunnel water inrush process at first. The principle of lattice Boltzmann method was introduced by introducing D2Q9 model. In order to improve the reliability and accuracy of simulation, we choose the G2Q9 model is to handle incompressible fluid like water, which was proposed by Guo. We choose different solutions to deal with boundary treatment according different boundary conditions. The bounce-back scheme on a straight boundary and the BFL scheme on a curved boundary were adopted respectively. Because of the complex of tunnel structure, we use separated-coupled algorithm to handle the corresponding boundary in order to reduce computation and improve the efficiency of operations. Finally an example simulation was to verify our theory.
Then we simulate two methods that rescue the water inrush and proposed block-style simulation model and emission-style simulation model. For block-style simulation, we established a corresponding inrush block model, using the BFL to process the border. We get the press, speed, flow and other result of tunnel at different time according to the completion of retaining wall. After analysis these results, we think that the results is in line with our expectations. We also established the corresponding drainage model for emission-style simulation and use force to simulate the principles of pumps. And finally the results that instruct the press graph, speed chart ,flow charts and others was got by comparing the two conditions that are under the pressure and stress-free. The results meet our expectation.
Finally, in order to understanding about the role that simulate water inrush based on LBM method more clearly, we select D3Q15 model for three-dimensional water inrush simulation which based on the first and second chapters. A simulation case is also verifies our theory at last.
How to simplify the complex tunnel, how to select the appropriate Boltzmann models, how to deal with the grid boundaries, how to improve the efficiency of the program, how to get a satisfactory simulation results, all are the focus of the study. This study has also provided the reference and research basis for mine development, comprehensive management and related technology research.
通过阅读大量的文献资料,了解了目前国内外学者在地下突水方面的研究的现状,发现学者在突水数值模拟方面所做的研究相对来说少一些,其中以东北大学和中国矿业大学为主,且采用有限元方法结合FLAC软件进行模拟,解决方法较为单一。所以本文选择在诸多领域已经有很好研究成果的格子Boltzmann来对地下突水情况进行研究。
首先研究了一个二维巷道的突水过程。通过介绍D2Q9模型来向大家介绍格子Boltzmann的方法原理。为了提高模拟的可靠性和精度,我们选择了Guo等人提出的针对类似于水一样的不可压缩流体的G2Q9模型。在进行边界处理的时候,根据不同的边界情况,我们选择了不同的解决方法。对于平直边界来说,我们选用了修正的反弹格式进行处理,对于那些不规则的边界来说,我们选用BFL进行曲面边界的处理。同时由于巷道结构的复杂,为了降低运算量,提高运算的效率,我们使用分块耦合的方法对巷道进行了相应的处理。最后通过一个实例模拟来验证我们的理论。
其次针对突水抢救的两种方式进行了数值模拟,提出堵式模拟和疏式模拟模型。对于堵式模拟,我们建立了相应的突水阻滞模型,使用BFL进行边界的处理。通过模拟挡水墙的完成情况,我们得到了不同时刻的巷道内的压力、速度、流向等结果,分析这些结果,我们可以比较清楚的看到这种方法对于巷道内压力,速度,水流方向的改变都有一定的作用,符合我们的预期情况。对于疏式模拟,我们建立了相应的抽放模型,并使用作用力的方式来模拟抽水机的原理,最后通过对比有压力和无压力下的两种状况,得到的各种压力图,速度图,流线图等结果满足了我们的期望值。
最后为了直观清楚的了解LBM方法在巷道突水方面的模拟作用,我们在前两章的基础上,我们选用D3Q15模型来对三维巷道的突水情况进行模拟。最后也通过一个实例模拟来验证了我们的理论。
如何简化处理复杂的巷道问题,如何选用合适的Boltzmann模型,如何进行网格边界的处理,如何提高程序的运行效率,如何得到满意的仿真结果,这些都是本文的研究重点。本文的研究对于矿山开发,综合治理,以及相关技术的研究提供了方法参考和研究依据。
?Tunnel water-inrush in tunnel is a phenomenon that means groundwater in the bottom aquifer breaks mine seam or relatively impermeable layer between aquifers along faults, joints and other structural plane inrush mine suddenly, under the combined effects of factors such as the water pressure and rock pressure, when the mine was exploited Tunnel water-inrush is a induced geological disasters which related with engineering and mining activities. It is engineering geological problems. Large inrush of water is not only flooded mine tunnel , but also can cause collapse and rock unstable, or even result in disastrous results like personal injury and construction scrapped. So it has important guiding significance in improve mine safety and guarantee officers and properties for us selecting scientific method to study the water-inrush changes and movement law in tunnel.
I understand the research status in water-inrush from domestic and foreign scholars after reading large amount of literatures. And find that there is a relatively small number scholar to study water-inrush simulation, in which Northeastern University and China University of Mining and Technology are stay on top. They simulate the water-inrush combined the finite element method and FLAC software, the solution is relatively homogeneous. So the paper adapts Lattice Boltzmann Method to simulate tunnel water-inrush, which has a lot of great research result in many fields.
We study a two-dimensional tunnel water inrush process at first. The principle of lattice Boltzmann method was introduced by introducing D2Q9 model. In order to improve the reliability and accuracy of simulation, we choose the G2Q9 model is to handle incompressible fluid like water, which was proposed by Guo. We choose different solutions to deal with boundary treatment according different boundary conditions. The bounce-back scheme on a straight boundary and the BFL scheme on a curved boundary were adopted respectively. Because of the complex of tunnel structure, we use separated-coupled algorithm to handle the corresponding boundary in order to reduce computation and improve the efficiency of operations. Finally an example simulation was to verify our theory.
Then we simulate two methods that rescue the water inrush and proposed block-style simulation model and emission-style simulation model. For block-style simulation, we established a corresponding inrush block model, using the BFL to process the border. We get the press, speed, flow and other result of tunnel at different time according to the completion of retaining wall. After analysis these results, we think that the results is in line with our expectations. We also established the corresponding drainage model for emission-style simulation and use force to simulate the principles of pumps. And finally the results that instruct the press graph, speed chart ,flow charts and others was got by comparing the two conditions that are under the pressure and stress-free. The results meet our expectation.
Finally, in order to understanding about the role that simulate water inrush based on LBM method more clearly, we select D3Q15 model for three-dimensional water inrush simulation which based on the first and second chapters. A simulation case is also verifies our theory at last.
How to simplify the complex tunnel, how to select the appropriate Boltzmann models, how to deal with the grid boundaries, how to improve the efficiency of the program, how to get a satisfactory simulation results, all are the focus of the study. This study has also provided the reference and research basis for mine development, comprehensive management and related technology research.
引文
[1]潘晖,王继尧.基于粒子群优化神经网络的煤层底板突水预测[J].山西焦煤科技.2009,1(1):34~36.
[2]刘再斌,靳德武,刘其声.基于二项logistic回归模型与CART树的煤层底板突水预测[J].煤田地质与勘探.2009,37(1):56~61.
[3]邓书显,张学凌,饶明贵.基于Fuzzy逻辑和物元分析的矿井突水预测研究[J].江西理工大学学报.2009,30(4):1~3.
[4]施龙青,韩进,宋扬.用突水概率指数法预测采场底板突水[J].中国矿业大学学报.1999,28(5):442~444.
[5]廖巍,周荣义,李树清.基于小波神经网络的煤层底板突水非线性预测方法研究[J].中国安全科学学报.2006,16(11):24~28.
[6]高卫东,渠立权.基于GIS的煤层底板突水预测[J].测绘通报.2003,12.45~46
[7]程艳琴,王连车等.突变学理论在桃园矿10煤层底板突水预测中的应用[J].煤田地质与勘探.2007,2(35):45~48.
[8]禇营.灰色马尔柯夫模型在煤矿安全事故预测中的应用初探[J].能源技术与管理.2006(1):18-34.
[9]钱家忠,朱学愚,吴剑锋等.矿井涌水量的灰色马尔可夫预报模型[J].煤炭学报.2000,25(1):71-75.
[10]刘伟韬.底板突水预测专家系统研究[D].山东科技大学学位论文.2002.
[11]陈学星,刘伟韬,张文泉.预测底板突水的专家系统研究[J].煤矿自动化.2001,1:5-7.
[12]高延法,章延平等.底板突水危险性评价专家系统及应用研究[J].岩石力学与工程学报.2009,28(2):5-7.
[13]潘树仁,李宾亭,杨国勇等.煤矿水害防治专家系统[J].煤炭科技.1999,(4):12-13.
[14]岳梅.判断矿井突水水源灰色系统关联分析的应用[J].煤炭科学技术.2004:4
[15]李其康.灰色局势综合评判法在煤矿突水水源判别中的应用[J].中国煤炭地质.2008,20(7):47~48.
[16]张宏刚.灰色局势综合评判法在突水水源判别中的应用[J].水利科技与经济.2007,13(12):887~888.
[17]李明山.模糊相似比在判别矿井突水水源中的应用[J].煤炭工程师.1995,(1):28~31.
[18]樊京周,李化玉,谢拂晓.模糊概率法在识别矿井突水水源中的应用[J].中州煤炭.2006(6):1~2.
[19]李世峰,李耀华.模糊综合判别矿井突(涌)水水源[J].煤炭工程.2006,(9):71~73
[20]李明山,胡友彪等.姚桥煤矿矿井突水水源模糊综合评价模型[J].勘探科学技术.2001,(2):16~20.
[21]余克林,杨永生,章臣平.模糊综合评判法在判别矿井突水水源中的应用[J].金属矿山.2007,(3):47~50.
[22]贲旭东,郭英海,解奕伟等.模糊综合评判在矿井突水水源判别中的应用及探讨[J].矿业安全与环保.2006,33(3):57~59.
[23]李志锋,翟振.煤矿矿井突水水源的Fisher判别模型[J].矿业快报.2008,(9):57~58.
[24]陈红江,李夕兵,刘爱华等.用Fisher判别法确定矿井突水水源[J].中南大学学报(自然科学版).2008,40(4):1114~1119.
[25]闫志刚,白海波.矿井涌水水源识别的MMH支持向量机模型[J].岩石力学与工程学报.2009,28(2):324~329.
[26]闫志刚,杜培军,郭达志.矿井涌水水源分析的支持向量机模型[J].煤炭学报.2007,32(8):842~845.
[27]高卫东,何元东,李新社.水化学法在矿井突水水源判断中的应用[J].矿业安全与环保.2001,(10):44~45.
[28]煤矿水害防治水化学分析方法MT/T 672—1997[M].中国煤炭工业出版社.1998,(6).
[29]段玉成,黑磊,解光新.环境同位素在邢台煤矿放水试验中的应用[J].煤田地质与勘探.1994,22(1):33~37.
[30]武强,朱斌,李建民.“脆弱性指数法“在赵各庄矿底板突水评价中的应用[J].中国煤炭地质.2009,21(6):40~44.
[31]刘伟韬,张文泉,李加.用层次分析-模糊评判进行底板突水安全性评价[J].煤炭学报.2000,25(3):278~282.
[32]汪宏志,胡宝林,徐德金.基于GIS技术的煤层底板突水危险性综合评价[J].煤炭科学技术.2008,36(10):82~85.
[33]张文泉,刘伟韬,李家祥等.矿井水害防治专家系统[J].计算机工程.2000,26(5):83~85.
[34]刘洪磊,杨天鸿,朱万成等.范各庄矿5煤顶板破坏及突水模拟研究[J].采矿与安全工程学报.2009,26(3):332~335.
[35]冯启言,杨天鸿等.基于渗流损伤耦合分析的煤层底板突水过程的模拟[J].安全与环境学报.2006,6(3):1~4.
[36]杨天鸿,唐春安,刘红元等.承压水底板突水失稳过程的数值模型初探[J].地质力学学报.2003,9(3):281~287.
[37]武强,朱斌,李建民等.断裂带煤矿井巷滞后突水机理数值模拟[J].中国矿业大学学报.2008,37(6):780~785.
[38]王沁,姚令侃.一维粘性泥石流运动的格子Boltzmann模拟[J].灾害学.2007,12(4):1~4.
[39]王旭升,万力等.可承压地下水流的横向移动界面[J].自然科学进展.2008,11(11):1336~1340.
[40]王龙.圆柱绕流的LBM模拟[J].北京大学学报(自然科学版).2002,9(5):647~652.
[41]袁竹林,蔡桂英.圆柱绕流现象的格子玻耳兹曼数值模拟[J].中国电机工程学报.2004,8(8):162~165.
[42]郭照立,郑楚光等.基于Lattice Boltzmann方法圆柱绕流大涡模拟[J].工程热物理学报.2002,7(4):479~481.
[43]饶勇,倪玉山等.并列双方柱绕流的Lattice Boltzmann模拟分析[J].应用力学学报.2008,6(2).
[44]王兴勇,索丽生等.用Lattice Boltzmann方法模拟方柱绕流[J].河海大学学报(自然科学版).2003,5(3).
[45]赖惠林,马昌凤.二维对流扩散方程的格子BGK模拟[J].福建师范大学学报(自然科学版).2008,9(5):15~18.
[46]邓敏艺,刘慕仁等.二维反应扩散方程的格子Boltzmann方法模拟[J].广西师范大学学报(自然科学版).2001,3(1):1~5.
[47]张华,许桂生.二维分层流的格子Boltzmann数值模拟[J].水利学报.2006,11(11).
[48]闫广武.二维剪切流的格子boltzmann模拟[J].水动力学研究与进展.2003,9(5):521~525.
[49]程永光,索丽生.二维明渠非恒定流的格子boltzmann模拟[J].水科学进展.2003,4(1).
[50]唐桂华,何雅玲等.二维平板通道中流动与传热的格子boltzmann模拟[J].工程热物理学报.2003,11(6):995~997.
[51]唐秀英,吉玉嫔等.三维晶格玻尔兹曼方法模拟动脉弓内的流场[J].北京师范大学学报(自然科学版).2007,43(5).
[52]朱益华,陶果等.3D多孔介质渗透率的格子boltzmann模拟[J].测井技术.2008,32(1):25~28.
[53]邢玉飞,赵煜等.煤层瓦斯运移的模拟现状分析[J].科技信息.2009,(13).
[54]黄光球,乔坤,陆秋琴.基于元胞自动机的地下矿巷道系统中地下水突出与蔓延仿真方法[J].计算机工程.2007,33(14):219-224.
[55]陆秋琴,韦献刚等.基于格子Boltzmann方法的地下矿巷道系统热流态仿真[J].系统仿真学报.2010.2.28.
[56]王鹏,黄光球.基于LBM的地下矿突水蔓延仿真实现[D].西安:西安建筑科技大学.2010.
[57]Raghuprasad B.K.,Bhat D.N.,Bhattacharya G.S. Simulation of Fracture in a Quasi-brittle Material in Direct Tension–a Lattice Model,Engineering Fracture Mechanics,1998,61;445~460.
[58]Chen H, Chen S, Matthaeus W H. Recovery of the Navier-Stokes Equation Using Lattice-gas Blotzmann Method[J]. Phys Rev A, 1992, 45:5339-5342.
[59]Filippova O , Hanel D. Lat tice Boltzmann simulation of gas2particle flow in filters [ J ] . Comput Fluids , 1997 , 26 :697
[60]Bao-hua Guo. Numerical analysis on water-inrush process due to floor [ J ]. Journal of Coal Science and Engineering (China), 2008, 14(2):225-229
[61]He X Y, Chen S Y, Doolen G D.Numerical analysis of water inmsh from working-face flnoor during mining [J]. Journal of chian universicy of mining& technology 2008, 18(2):159-163
[62]Mei Rui , Wei Shi , Yu Da , et al . Lat tice Boltzmann method for 32D flows withcurved boundary [ J ] . JComput Phys , 2000 ,161 :680
[63]WOLF - GLADROW DA. Lattice - gas Cellular Automata and Lattice Boltzmann Models:An Introduction(Lecture Notes in Mathematics S)[M].Berlin Heidelberg:Springer - Verlag,2000:16
[64]HouS,ZouQ,ChenSY,etal.Simulation of Cavity Flow by the Lattice Boltzmann Method.Journal of Compu 2 tational Physics,1995,118:329～347
[2]刘再斌,靳德武,刘其声.基于二项logistic回归模型与CART树的煤层底板突水预测[J].煤田地质与勘探.2009,37(1):56~61.
[3]邓书显,张学凌,饶明贵.基于Fuzzy逻辑和物元分析的矿井突水预测研究[J].江西理工大学学报.2009,30(4):1~3.
[4]施龙青,韩进,宋扬.用突水概率指数法预测采场底板突水[J].中国矿业大学学报.1999,28(5):442~444.
[5]廖巍,周荣义,李树清.基于小波神经网络的煤层底板突水非线性预测方法研究[J].中国安全科学学报.2006,16(11):24~28.
[6]高卫东,渠立权.基于GIS的煤层底板突水预测[J].测绘通报.2003,12.45~46
[7]程艳琴,王连车等.突变学理论在桃园矿10煤层底板突水预测中的应用[J].煤田地质与勘探.2007,2(35):45~48.
[8]禇营.灰色马尔柯夫模型在煤矿安全事故预测中的应用初探[J].能源技术与管理.2006(1):18-34.
[9]钱家忠,朱学愚,吴剑锋等.矿井涌水量的灰色马尔可夫预报模型[J].煤炭学报.2000,25(1):71-75.
[10]刘伟韬.底板突水预测专家系统研究[D].山东科技大学学位论文.2002.
[11]陈学星,刘伟韬,张文泉.预测底板突水的专家系统研究[J].煤矿自动化.2001,1:5-7.
[12]高延法,章延平等.底板突水危险性评价专家系统及应用研究[J].岩石力学与工程学报.2009,28(2):5-7.
[13]潘树仁,李宾亭,杨国勇等.煤矿水害防治专家系统[J].煤炭科技.1999,(4):12-13.
[14]岳梅.判断矿井突水水源灰色系统关联分析的应用[J].煤炭科学技术.2004:4
[15]李其康.灰色局势综合评判法在煤矿突水水源判别中的应用[J].中国煤炭地质.2008,20(7):47~48.
[16]张宏刚.灰色局势综合评判法在突水水源判别中的应用[J].水利科技与经济.2007,13(12):887~888.
[17]李明山.模糊相似比在判别矿井突水水源中的应用[J].煤炭工程师.1995,(1):28~31.
[18]樊京周,李化玉,谢拂晓.模糊概率法在识别矿井突水水源中的应用[J].中州煤炭.2006(6):1~2.
[19]李世峰,李耀华.模糊综合判别矿井突(涌)水水源[J].煤炭工程.2006,(9):71~73
[20]李明山,胡友彪等.姚桥煤矿矿井突水水源模糊综合评价模型[J].勘探科学技术.2001,(2):16~20.
[21]余克林,杨永生,章臣平.模糊综合评判法在判别矿井突水水源中的应用[J].金属矿山.2007,(3):47~50.
[22]贲旭东,郭英海,解奕伟等.模糊综合评判在矿井突水水源判别中的应用及探讨[J].矿业安全与环保.2006,33(3):57~59.
[23]李志锋,翟振.煤矿矿井突水水源的Fisher判别模型[J].矿业快报.2008,(9):57~58.
[24]陈红江,李夕兵,刘爱华等.用Fisher判别法确定矿井突水水源[J].中南大学学报(自然科学版).2008,40(4):1114~1119.
[25]闫志刚,白海波.矿井涌水水源识别的MMH支持向量机模型[J].岩石力学与工程学报.2009,28(2):324~329.
[26]闫志刚,杜培军,郭达志.矿井涌水水源分析的支持向量机模型[J].煤炭学报.2007,32(8):842~845.
[27]高卫东,何元东,李新社.水化学法在矿井突水水源判断中的应用[J].矿业安全与环保.2001,(10):44~45.
[28]煤矿水害防治水化学分析方法MT/T 672—1997[M].中国煤炭工业出版社.1998,(6).
[29]段玉成,黑磊,解光新.环境同位素在邢台煤矿放水试验中的应用[J].煤田地质与勘探.1994,22(1):33~37.
[30]武强,朱斌,李建民.“脆弱性指数法“在赵各庄矿底板突水评价中的应用[J].中国煤炭地质.2009,21(6):40~44.
[31]刘伟韬,张文泉,李加.用层次分析-模糊评判进行底板突水安全性评价[J].煤炭学报.2000,25(3):278~282.
[32]汪宏志,胡宝林,徐德金.基于GIS技术的煤层底板突水危险性综合评价[J].煤炭科学技术.2008,36(10):82~85.
[33]张文泉,刘伟韬,李家祥等.矿井水害防治专家系统[J].计算机工程.2000,26(5):83~85.
[34]刘洪磊,杨天鸿,朱万成等.范各庄矿5煤顶板破坏及突水模拟研究[J].采矿与安全工程学报.2009,26(3):332~335.
[35]冯启言,杨天鸿等.基于渗流损伤耦合分析的煤层底板突水过程的模拟[J].安全与环境学报.2006,6(3):1~4.
[36]杨天鸿,唐春安,刘红元等.承压水底板突水失稳过程的数值模型初探[J].地质力学学报.2003,9(3):281~287.
[37]武强,朱斌,李建民等.断裂带煤矿井巷滞后突水机理数值模拟[J].中国矿业大学学报.2008,37(6):780~785.
[38]王沁,姚令侃.一维粘性泥石流运动的格子Boltzmann模拟[J].灾害学.2007,12(4):1~4.
[39]王旭升,万力等.可承压地下水流的横向移动界面[J].自然科学进展.2008,11(11):1336~1340.
[40]王龙.圆柱绕流的LBM模拟[J].北京大学学报(自然科学版).2002,9(5):647~652.
[41]袁竹林,蔡桂英.圆柱绕流现象的格子玻耳兹曼数值模拟[J].中国电机工程学报.2004,8(8):162~165.
[42]郭照立,郑楚光等.基于Lattice Boltzmann方法圆柱绕流大涡模拟[J].工程热物理学报.2002,7(4):479~481.
[43]饶勇,倪玉山等.并列双方柱绕流的Lattice Boltzmann模拟分析[J].应用力学学报.2008,6(2).
[44]王兴勇,索丽生等.用Lattice Boltzmann方法模拟方柱绕流[J].河海大学学报(自然科学版).2003,5(3).
[45]赖惠林,马昌凤.二维对流扩散方程的格子BGK模拟[J].福建师范大学学报(自然科学版).2008,9(5):15~18.
[46]邓敏艺,刘慕仁等.二维反应扩散方程的格子Boltzmann方法模拟[J].广西师范大学学报(自然科学版).2001,3(1):1~5.
[47]张华,许桂生.二维分层流的格子Boltzmann数值模拟[J].水利学报.2006,11(11).
[48]闫广武.二维剪切流的格子boltzmann模拟[J].水动力学研究与进展.2003,9(5):521~525.
[49]程永光,索丽生.二维明渠非恒定流的格子boltzmann模拟[J].水科学进展.2003,4(1).
[50]唐桂华,何雅玲等.二维平板通道中流动与传热的格子boltzmann模拟[J].工程热物理学报.2003,11(6):995~997.
[51]唐秀英,吉玉嫔等.三维晶格玻尔兹曼方法模拟动脉弓内的流场[J].北京师范大学学报(自然科学版).2007,43(5).
[52]朱益华,陶果等.3D多孔介质渗透率的格子boltzmann模拟[J].测井技术.2008,32(1):25~28.
[53]邢玉飞,赵煜等.煤层瓦斯运移的模拟现状分析[J].科技信息.2009,(13).
[54]黄光球,乔坤,陆秋琴.基于元胞自动机的地下矿巷道系统中地下水突出与蔓延仿真方法[J].计算机工程.2007,33(14):219-224.
[55]陆秋琴,韦献刚等.基于格子Boltzmann方法的地下矿巷道系统热流态仿真[J].系统仿真学报.2010.2.28.
[56]王鹏,黄光球.基于LBM的地下矿突水蔓延仿真实现[D].西安:西安建筑科技大学.2010.
[57]Raghuprasad B.K.,Bhat D.N.,Bhattacharya G.S. Simulation of Fracture in a Quasi-brittle Material in Direct Tension–a Lattice Model,Engineering Fracture Mechanics,1998,61;445~460.
[58]Chen H, Chen S, Matthaeus W H. Recovery of the Navier-Stokes Equation Using Lattice-gas Blotzmann Method[J]. Phys Rev A, 1992, 45:5339-5342.
[59]Filippova O , Hanel D. Lat tice Boltzmann simulation of gas2particle flow in filters [ J ] . Comput Fluids , 1997 , 26 :697
[60]Bao-hua Guo. Numerical analysis on water-inrush process due to floor [ J ]. Journal of Coal Science and Engineering (China), 2008, 14(2):225-229
[61]He X Y, Chen S Y, Doolen G D.Numerical analysis of water inmsh from working-face flnoor during mining [J]. Journal of chian universicy of mining& technology 2008, 18(2):159-163
[62]Mei Rui , Wei Shi , Yu Da , et al . Lat tice Boltzmann method for 32D flows withcurved boundary [ J ] . JComput Phys , 2000 ,161 :680
[63]WOLF - GLADROW DA. Lattice - gas Cellular Automata and Lattice Boltzmann Models:An Introduction(Lecture Notes in Mathematics S)[M].Berlin Heidelberg:Springer - Verlag,2000:16
[64]HouS,ZouQ,ChenSY,etal.Simulation of Cavity Flow by the Lattice Boltzmann Method.Journal of Compu 2 tational Physics,1995,118:329～347