河网溃堤与溃堤波的一、二维耦合数值模拟
|
摘要
水库一旦发生溃坝，其水头高，破坏力大，任何一座大坝若发生溃坝事故，都将造成极为严重的后果，给下游人民的生命财产带来严重危害。尤其在长江三角洲地区，河道交织成网，河网密度达614～617公里/平方公里以上，成为全国河网最稠密的地区。尤其河网地区又有许多圩区，一般地势低洼，都是由河道的防护堤岸来保护的，暴雨时泵站将圩区的水抽入外河排泄，外河水位往往高于圩区地面，所以预测河网地区由于局部圩区堤岸溃决造成的后果，是近年来研究的热点。本文对于河网采用Preissmann四点隐式差分格式计算，对于溃口及圩区采用有限体积法，建立的河网溃堤与溃堤波的一、二维耦合计算水力模型实现了真正意义上的一维河网计算向二维河网计算水域的过渡，模拟了河网溃堤过程中流场的变化情况、以及溃堤波传播过程中的传播、绕射、反射及变形等运动特征，模拟比较接近真实溃堤过程。其研究成果能较好的预测圩区淹没过程和淹没范围，为建立河流洪水预警系统提供了可靠的理论基础，同时也为溃堤灾害性分析和防灾减灾提供科学的依据，具有较大的指导意义。
Once the reservoir is breached,the dike-break long waves cause great damage to the people's life and property who lives in the downriver area.especially in the Yangzi River downriver where it has the thickest river network.The density of the network even comes to 614～617km/km~2,and there are lots of low-lying fields in the network
area.The protected bank is used to protect the area.The pumping station will drain the water from the low-lying field to the outside river,the water surface in the outside river is higher than it is in the low-lying field.So it becomes a hotspot to forecast the results brought by the past-areas'dike-break waves.In the paper,the hydraulic model of coupling 1 -D river network and 2-D dike-break waves really realizes the transition from 1-D calculation water area to 2-D water area,and it shows the process of river dike-breaking,the velocity variation of the breach flow and the flow characteristic of diffraction,refiection and deformation during the propagation of dike-break waves.The simulation can realistically show the burst process of the dike.It is conclude that the model can predict the submerge process and area effectively,provide academic base for establishment of flood forecast system and it has scientific decision reference and practical significance for flood warning service,.and also provides scientific basis for the analysis and prevention of disaster caused by dike destruction.
Once the reservoir is breached,the dike-break long waves cause great damage to the people's life and property who lives in the downriver area.especially in the Yangzi River downriver where it has the thickest river network.The density of the network even comes to 614～617km/km~2,and there are lots of low-lying fields in the network
area.The protected bank is used to protect the area.The pumping station will drain the water from the low-lying field to the outside river,the water surface in the outside river is higher than it is in the low-lying field.So it becomes a hotspot to forecast the results brought by the past-areas'dike-break waves.In the paper,the hydraulic model of coupling 1 -D river network and 2-D dike-break waves really realizes the transition from 1-D calculation water area to 2-D water area,and it shows the process of river dike-breaking,the velocity variation of the breach flow and the flow characteristic of diffraction,refiection and deformation during the propagation of dike-break waves.The simulation can realistically show the burst process of the dike.It is conclude that the model can predict the submerge process and area effectively,provide academic base for establishment of flood forecast system and it has scientific decision reference and practical significance for flood warning service,.and also provides scientific basis for the analysis and prevention of disaster caused by dike destruction.
引文
[1] 王嘉松，倪汉根，金生．瞬间全溃溃堤波的传播、反射和绕射的数值模拟[J]．水动力学研究与进展，2000，15(1)：1～7
[2] Wang J S, Ni H G, He Y S. Finite-difference TVD scheme for computation of dam-break problems[J]. Journal of Hydraulic Engineering, 2000, 126(4):253～262
[3] Aureli F, Mignosa P, Tomirotti M. Numerical simulation and experimental verification of dam-break flows with shocks[J]. Journal of Hydraulic Research, 2000, 38(3):197～206
[4] 谢任之．溃堤水力学[M]．山东科学技术出版社，1992．2
[5] Nikolaos Katopoders Theoder swelkoff 二维溃堤洪水波的计算Journal of Hydraulics Division ASCEVol．104 No Hy 9 1978．P.1269～1287
[6] 徐玉英，宋榜科，韩晓东等．水库下游无水位资料时淹没水位的计算[J]．水利水电技术，1999，30(1)：77～78
[7] Ritter, A. Die Fortpflanzung der Wasserwel-len [The propagation of water waves] Ver. Deutsch Ingenieure Zeitschr[M]. Berlin, 1892, 36(33):947～954
[8] 谢任之．溃堤坝址流量计算[M]．水利水运科学研究，1982(1)
[9] 汪德爟．计算水力学理论与应用[M]．河海大学出版社，1989：140，158～165
[10] 王忆龙，吴文明，孙宗胜．关于水力计算糙率系数确定方法的探讨[J]．黑龙江水利科技，1999，(4)：13～14
[11] 姜淑昆，付艳红．河道糙率问题的探讨[J]．吉林水利，2005，271(3)：25～26
[12] 余树华，李建梅．浅谈河床糙率的分析方法[J]．甘肃水利水电技术，2006，42(2)：169～170
[13] 武汉水利电力学院，华东水利学院．水力学[M]．北京人民教育出版社，1979
[14] 韩龙喜，金忠青．三级联解法水力水质模型的糙率反演及面污染源计算[J]．水利学报，1998，(7)：30～34
[15] 石国钰，叶敏，唐佩文．堤防分洪溃口变化特征初探[J]．人民长江，1997，28(1)：30～32
[16] 孔晋豫．溃堤洪水数学模型的初步应用[J]．电力勘测，1995．9，(3)：53～57
[17] 赵太平．水电工程溃堤洪水计算[J]．泥沙研究，2003，(2)：48～53
[18] 谭维炎．计算浅水动力学．有限体积法的应用[M]．北京：清华大学出版社，1998
[19] 史宏达，刘臻．溃堤水流数值模拟研究进展[J]．水科学进展，2006，17(1)
[20] 陶文铨．数值传热学[M]．西安：西安交通大学出版社，1988
[21] Patankar S V, Spalding D B. A Calculation Procedures for Heat,Mass and Momentum Transfer in Three-Dimensional Parabolic Flows[J]. Int .J. Heat and Mass Transfer,1972, 15: 1787-1806.
[22] Rhie C M, Chow W L. A Numerical Study of the Turbulent Flow Past an Isolated Airfoil With Trailing Edge Seperation[J]. AIAA J.,1983, 21:1525-1532.
[23] Peric M, Kessler R, Scheuerer G. Comparison of Finite-Volume Numerical Methods Wiih Stagger~d and Collocated Grids[J]. Computers and Fluids, 1988, 16(4):389～403.
[24] Miller T F, Schmidt F W. Use of a Pressure-Weighted Interpolation Method for Solution of the Incompressible Navier-stokes Equations on a Nonstaggered Grid System[J]. Numerical HeatTransfer, 1988, 14:213～233.
[25] Rodi W, Majumdar S and Schonung B. Finite-Volume Methods for Two-dimensional Incompressible Flows With complex Boundaries[J]. Comput. Meth. Appl. Meth. Eng.,1989, 75:369～392.
[26] Thiart G.D. Finite-Difference Scheme for the Numerical Solution of Fluid Flow and Heat Transfer Problems on Nonstaggered grid[J]. Numerical Heat Transfer, 1990, 17B,43～62.
[27] ZHAO D H, SHEN H W, TABIOS Ⅲ G Q, LAI J S. andTAN W Y. Finite-volume two-dimensional unsteady-flow model for fiver basins[J]. Hydr. Engrg, ASCE,1994, 120(7) :863～883.
[28] ZHAO D H, SHEN H W, LAI J S, et al. Approximate Riemann solvers in FVM for 2D hydraulic shock waves modeling[J]. Hydr. Engrg., ASCE, 1996, 122(12):693～702.
[29] 赵棣华，戚晨，庾维德，徐保华，裴中平．平面二维水流水质有限体积法及黎曼近似界模型[J]．水科学进展，2000，11(4)：368～373．
[30] ZHAO D H, et al. 2D-FVM model for modeling riverbed deformation due to cutoff [A]. Proceedings of International Conference on Hydraulic Engineering[C]. Iowa, US., 1999
[31] 赵棣华，沈福新，颜志俊，卢恭和．基于有限体积法及FDS格式的感潮河段二维泥沙冲淤模型[J]．水动力学研究与进展A辑，2004，19．：98-103．
[32] Wurbs R A. Dam-break flood wave models[J], Journal of Hydraulic Engineering, ASCE, 1987, 113(1): 29～46
[33] 朱自强等．应用计算流体力学[M]．北京航空航天大学出版社，1997，7：66～70
[34] 傅德熏等．流体力学数值模拟[M]．国防大学出版社，1993，11
[35] Van Leer B. On the relation between the upwind-differencing schemes of Godunov, Enguist-Osher and Roe[J]. SIAM Journal of Science and Statistical Computations, 1985,5(1): 1～20
[36] Roe P L. Generalized formulation of TVD Lax-Wen&off schemes[J]. ICASE Report No.84-53, 1984
[37] Van Leer B, Thomas J L, Roe P L, Newasome T W. A comparison of numerical flux formulas for the Euler and Navier-Stokes equations[J]. AIAA 87-1104
[38] 水鸿寿．一维流体力学差分方法[M]．国防工业出版社，1998．2
[39] 王志刚．实际地形溃堤水流的数值模拟[M]．河海大学硕士学位论文，2003：15～16
[40] 刘儒勋，王志峰等．数值模拟方法和运动界面追踪[M]．中国科技大学出版社，2001．10
[41] Courant R, Friedrich K O, Lewy H. On the partial differential equation of mathematical physics[J]. IBM Journal, 1967, 11(2): 215～234
[42] 谭维炎，胡四一．二维浅水流动的一种普适的高性能格式[J]．水科学进展，2000，2(3)
[43] 谭维炎，胡四一．浅水流动计算中一阶有限体积法Osher格式的实现[J]．水科学进展，，1994，5(4)：262．269
[44] 杨丽．河网与湖泊耦联的水力水质数值模拟的研究与应用[M]．河海大学硕士学位论文，2003：56～57
[45] Zhao D H et al. Finite-volume two-dimensional unsteady-flow model for fiver basins[J]. ASCE J. Hydraul. Eng, 1994, 120:864～883
[46] Zhao D H et al. Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling[J]. J. Hydraulic Engineering, ASCE, 1996, 122(12):692～702
[47] Van Leer B. On the relation between the upwind-differencing schemes of Godunov, Enguist-Osher and Roe[J]. SIAM Journal of Science and Statistical Computations, 1985,5(1): 1～20
[48] 水鸿寿．一维流体力学差分方法[M]．国防工业出版社，1998．2
[49] Yee H C. Upwind and symmetric shock capturing schemes. NASA TM 89464, 1987
[50] 王志刚．实际地形溃堤水流的数值模拟[M]．河海大学硕士学位论文，2003：15～16
[51] Toro EE Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag: Berlin, Heidlberg, 1997
[52] 朱幼兰 钟锡昌 陈炳木等 初边值问题差分方法及绕流 科学出版社，1980
[53] Moretti G. Three-dimensional supersonic steady flows with any number of imbedded shocks. AIAA Paper No.74-10, 1974
[54] Steger J and Warming R E Flux vector splitting of the inviscid gas-dynamics equations with application to finite methods. NASA TMD-78605, 1979
[55] 傅德薰 马延文 气动计算中一个简单有效的差分格式 空气动力学学报，1985(2)
[56] 马延文 傅德薰 数值计算可压缩Nailer-Stokes方程的一个新的系数矩阵分裂法 计算物理，1985(2)
[57] 傅德薰．流体力学数值模拟．北京：国防工业出版社，1993
[58] 刘顺隆，郑群．计算流体力学．哈尔滨工程大学出版社，1998
[59] Garten A. On a class of high resolution total-variation-stable finite-difference schemes. NYU Report, Oct.1982
[60] Roe P L. Some contributions to the modeling of discontinuous flows. AMS-SIAM Seminar, Sam Diego, June 1983
[61] Var Leer B. Towards the uitimate conservative difference scheme. Journal of Computational Physics.1974(14): 363～389
[62] Osher S. Shock modeling in transonic and supersonic flow recent advances in numerical methods in fluids. Vol.4, W.GHabashi Ed
[63] Yee H C, Wanning R F and Harten A. Implicit total variation diminishing (TVD) schemes for steady-state calculations. AIAA Paper 83-1902, 1983
[64] Desiseri D and Jameson A. Multigrid solution of the Euler equations on unstructured and adaptive meshes. AIAA Paper 87-0353, 1987
[65] Pan D and Cheng J. Incompressible flow solution on unstructured triangular meshes. Int. J. Numer. Methods Fluids. 19939(16): 1079～1098
[66] Zhao D H et al. Finite-volume two-dimensional unsteady-flow model for fiver basins. ASCE J. Hydraul. Eng. 1994 (120) : 864～883
[67] Auastasiou K and Chan C T. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes. Int. J. Numer. Methods Fluids. 1997(24): 1225～1245
[68] 汪继文 刘儒勋 间断解问题的有限体积法 计算物理 Vol．18，No．2 Mar．，2001：97～105
[2] Wang J S, Ni H G, He Y S. Finite-difference TVD scheme for computation of dam-break problems[J]. Journal of Hydraulic Engineering, 2000, 126(4):253～262
[3] Aureli F, Mignosa P, Tomirotti M. Numerical simulation and experimental verification of dam-break flows with shocks[J]. Journal of Hydraulic Research, 2000, 38(3):197～206
[4] 谢任之．溃堤水力学[M]．山东科学技术出版社，1992．2
[5] Nikolaos Katopoders Theoder swelkoff 二维溃堤洪水波的计算Journal of Hydraulics Division ASCEVol．104 No Hy 9 1978．P.1269～1287
[6] 徐玉英，宋榜科，韩晓东等．水库下游无水位资料时淹没水位的计算[J]．水利水电技术，1999，30(1)：77～78
[7] Ritter, A. Die Fortpflanzung der Wasserwel-len [The propagation of water waves] Ver. Deutsch Ingenieure Zeitschr[M]. Berlin, 1892, 36(33):947～954
[8] 谢任之．溃堤坝址流量计算[M]．水利水运科学研究，1982(1)
[9] 汪德爟．计算水力学理论与应用[M]．河海大学出版社，1989：140，158～165
[10] 王忆龙，吴文明，孙宗胜．关于水力计算糙率系数确定方法的探讨[J]．黑龙江水利科技，1999，(4)：13～14
[11] 姜淑昆，付艳红．河道糙率问题的探讨[J]．吉林水利，2005，271(3)：25～26
[12] 余树华，李建梅．浅谈河床糙率的分析方法[J]．甘肃水利水电技术，2006，42(2)：169～170
[13] 武汉水利电力学院，华东水利学院．水力学[M]．北京人民教育出版社，1979
[14] 韩龙喜，金忠青．三级联解法水力水质模型的糙率反演及面污染源计算[J]．水利学报，1998，(7)：30～34
[15] 石国钰，叶敏，唐佩文．堤防分洪溃口变化特征初探[J]．人民长江，1997，28(1)：30～32
[16] 孔晋豫．溃堤洪水数学模型的初步应用[J]．电力勘测，1995．9，(3)：53～57
[17] 赵太平．水电工程溃堤洪水计算[J]．泥沙研究，2003，(2)：48～53
[18] 谭维炎．计算浅水动力学．有限体积法的应用[M]．北京：清华大学出版社，1998
[19] 史宏达，刘臻．溃堤水流数值模拟研究进展[J]．水科学进展，2006，17(1)
[20] 陶文铨．数值传热学[M]．西安：西安交通大学出版社，1988
[21] Patankar S V, Spalding D B. A Calculation Procedures for Heat,Mass and Momentum Transfer in Three-Dimensional Parabolic Flows[J]. Int .J. Heat and Mass Transfer,1972, 15: 1787-1806.
[22] Rhie C M, Chow W L. A Numerical Study of the Turbulent Flow Past an Isolated Airfoil With Trailing Edge Seperation[J]. AIAA J.,1983, 21:1525-1532.
[23] Peric M, Kessler R, Scheuerer G. Comparison of Finite-Volume Numerical Methods Wiih Stagger~d and Collocated Grids[J]. Computers and Fluids, 1988, 16(4):389～403.
[24] Miller T F, Schmidt F W. Use of a Pressure-Weighted Interpolation Method for Solution of the Incompressible Navier-stokes Equations on a Nonstaggered Grid System[J]. Numerical HeatTransfer, 1988, 14:213～233.
[25] Rodi W, Majumdar S and Schonung B. Finite-Volume Methods for Two-dimensional Incompressible Flows With complex Boundaries[J]. Comput. Meth. Appl. Meth. Eng.,1989, 75:369～392.
[26] Thiart G.D. Finite-Difference Scheme for the Numerical Solution of Fluid Flow and Heat Transfer Problems on Nonstaggered grid[J]. Numerical Heat Transfer, 1990, 17B,43～62.
[27] ZHAO D H, SHEN H W, TABIOS Ⅲ G Q, LAI J S. andTAN W Y. Finite-volume two-dimensional unsteady-flow model for fiver basins[J]. Hydr. Engrg, ASCE,1994, 120(7) :863～883.
[28] ZHAO D H, SHEN H W, LAI J S, et al. Approximate Riemann solvers in FVM for 2D hydraulic shock waves modeling[J]. Hydr. Engrg., ASCE, 1996, 122(12):693～702.
[29] 赵棣华，戚晨，庾维德，徐保华，裴中平．平面二维水流水质有限体积法及黎曼近似界模型[J]．水科学进展，2000，11(4)：368～373．
[30] ZHAO D H, et al. 2D-FVM model for modeling riverbed deformation due to cutoff [A]. Proceedings of International Conference on Hydraulic Engineering[C]. Iowa, US., 1999
[31] 赵棣华，沈福新，颜志俊，卢恭和．基于有限体积法及FDS格式的感潮河段二维泥沙冲淤模型[J]．水动力学研究与进展A辑，2004，19．：98-103．
[32] Wurbs R A. Dam-break flood wave models[J], Journal of Hydraulic Engineering, ASCE, 1987, 113(1): 29～46
[33] 朱自强等．应用计算流体力学[M]．北京航空航天大学出版社，1997，7：66～70
[34] 傅德熏等．流体力学数值模拟[M]．国防大学出版社，1993，11
[35] Van Leer B. On the relation between the upwind-differencing schemes of Godunov, Enguist-Osher and Roe[J]. SIAM Journal of Science and Statistical Computations, 1985,5(1): 1～20
[36] Roe P L. Generalized formulation of TVD Lax-Wen&off schemes[J]. ICASE Report No.84-53, 1984
[37] Van Leer B, Thomas J L, Roe P L, Newasome T W. A comparison of numerical flux formulas for the Euler and Navier-Stokes equations[J]. AIAA 87-1104
[38] 水鸿寿．一维流体力学差分方法[M]．国防工业出版社，1998．2
[39] 王志刚．实际地形溃堤水流的数值模拟[M]．河海大学硕士学位论文，2003：15～16
[40] 刘儒勋，王志峰等．数值模拟方法和运动界面追踪[M]．中国科技大学出版社，2001．10
[41] Courant R, Friedrich K O, Lewy H. On the partial differential equation of mathematical physics[J]. IBM Journal, 1967, 11(2): 215～234
[42] 谭维炎，胡四一．二维浅水流动的一种普适的高性能格式[J]．水科学进展，2000，2(3)
[43] 谭维炎，胡四一．浅水流动计算中一阶有限体积法Osher格式的实现[J]．水科学进展，，1994，5(4)：262．269
[44] 杨丽．河网与湖泊耦联的水力水质数值模拟的研究与应用[M]．河海大学硕士学位论文，2003：56～57
[45] Zhao D H et al. Finite-volume two-dimensional unsteady-flow model for fiver basins[J]. ASCE J. Hydraul. Eng, 1994, 120:864～883
[46] Zhao D H et al. Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling[J]. J. Hydraulic Engineering, ASCE, 1996, 122(12):692～702
[47] Van Leer B. On the relation between the upwind-differencing schemes of Godunov, Enguist-Osher and Roe[J]. SIAM Journal of Science and Statistical Computations, 1985,5(1): 1～20
[48] 水鸿寿．一维流体力学差分方法[M]．国防工业出版社，1998．2
[49] Yee H C. Upwind and symmetric shock capturing schemes. NASA TM 89464, 1987
[50] 王志刚．实际地形溃堤水流的数值模拟[M]．河海大学硕士学位论文，2003：15～16
[51] Toro EE Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag: Berlin, Heidlberg, 1997
[52] 朱幼兰 钟锡昌 陈炳木等 初边值问题差分方法及绕流 科学出版社，1980
[53] Moretti G. Three-dimensional supersonic steady flows with any number of imbedded shocks. AIAA Paper No.74-10, 1974
[54] Steger J and Warming R E Flux vector splitting of the inviscid gas-dynamics equations with application to finite methods. NASA TMD-78605, 1979
[55] 傅德薰 马延文 气动计算中一个简单有效的差分格式 空气动力学学报，1985(2)
[56] 马延文 傅德薰 数值计算可压缩Nailer-Stokes方程的一个新的系数矩阵分裂法 计算物理，1985(2)
[57] 傅德薰．流体力学数值模拟．北京：国防工业出版社，1993
[58] 刘顺隆，郑群．计算流体力学．哈尔滨工程大学出版社，1998
[59] Garten A. On a class of high resolution total-variation-stable finite-difference schemes. NYU Report, Oct.1982
[60] Roe P L. Some contributions to the modeling of discontinuous flows. AMS-SIAM Seminar, Sam Diego, June 1983
[61] Var Leer B. Towards the uitimate conservative difference scheme. Journal of Computational Physics.1974(14): 363～389
[62] Osher S. Shock modeling in transonic and supersonic flow recent advances in numerical methods in fluids. Vol.4, W.GHabashi Ed
[63] Yee H C, Wanning R F and Harten A. Implicit total variation diminishing (TVD) schemes for steady-state calculations. AIAA Paper 83-1902, 1983
[64] Desiseri D and Jameson A. Multigrid solution of the Euler equations on unstructured and adaptive meshes. AIAA Paper 87-0353, 1987
[65] Pan D and Cheng J. Incompressible flow solution on unstructured triangular meshes. Int. J. Numer. Methods Fluids. 19939(16): 1079～1098
[66] Zhao D H et al. Finite-volume two-dimensional unsteady-flow model for fiver basins. ASCE J. Hydraul. Eng. 1994 (120) : 864～883
[67] Auastasiou K and Chan C T. Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes. Int. J. Numer. Methods Fluids. 1997(24): 1225～1245
[68] 汪继文 刘儒勋 间断解问题的有限体积法 计算物理 Vol．18，No．2 Mar．，2001：97～105