粉沙淤泥质海岸水流泥沙数学模型理论及工程应用
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摘要
本文结合当前港口建设中所关注的粉沙淤泥质海岸建港问题进行了主要研究。在文章中结合粉沙质沙的特性对粉沙淤泥质海岸进行定义,同时分析了该海岸类型下的泥沙运动特点,在总结前人研究理论的基础上提出了自己的研究方法。
泥沙运动特点是港口海岸建设工程中必然要考虑的问题,本文由粉沙淤泥质海岸泥沙运动特点建立起水流泥沙方程,根据粉沙质泥沙特性分别建立悬移质、推移质输沙方程,以及床面变形方程,对于泥沙冲淤模型采用平衡挟沙的原理进行计算,希望能提出一个合理有效的计算模型。与此同时,采用二维迎风有限元方法解决二维水流泥沙问题,用三角形网格对计算区域进行剖分,同时为了节省计算机内存,采用集中质量法进行计算。
在建立模型过程中,对于模型方程中有关物理量的确定,在以往研究的基础上又进行了进一步的改进,对前人的工作进行了发展与延伸,同时对海床稳定性条件进行了研究,给出了床面处于不冲不淤的稳定平衡状态的条件,对海床的稳定性判别给出了一个较为具体的判定条件。
最后,为了对所建数学模型进行验证,针对所提出的二维水流泥沙数学模型方程,编制计算程序,并将程序运用于福清湾元载码头三期扩建潮流泥沙计算,结合计算结果对工程的布置及规模确定给予适当的建议,并且希望在此研究基础上该模型能够对粉沙淤泥质海岸泥沙运动特性研究有所帮助,特别是针对于潮流动力作用很强的粉沙淤泥质海岸河口。
This paper is based on the problem that how to construct port structure on silty mud coast which is a very difficult and hot problem at present. A definition to silty mud coast and a new method on research are given, at the same time the characteristics of sediment transport based on the theories that are wildly accepted is analysised.
It is necessary to consider the feature of sediment transport in the port engineering construction, and in this paper a set of the flow-sediment equations which is based the properties of sediment transport on the silty mud coast are established. By the same way, the suspended load and traction load equations and bed surface deformation equation are established.Balance sediment-carrying principle is used in order to give a reasonable calculation model. Meanwhile, two-dimension upwind finite element is used to solve the flow-sediment calculation, and the grid is triangular grid. Lumped mass method is used to saves computer memory.
During the course of modeling building, a further improvement on the physical quantities that are furthermore development and extension based on the previous works is given in this paper. The stability condition of sea bed is studied and a equilibrium condition which provides the judgement of seabed stability is offered.
Finally, in order to test the model, program based on the flow-sediment equations is written and applied.In this paper proper suggestions is given on the construction of ports.It is hoped that the conclusion will be useful in the future research of silty mud coast especially in the research on the coast and estuary where the influence of tide is stronger than wave.
泥沙运动特点是港口海岸建设工程中必然要考虑的问题,本文由粉沙淤泥质海岸泥沙运动特点建立起水流泥沙方程,根据粉沙质泥沙特性分别建立悬移质、推移质输沙方程,以及床面变形方程,对于泥沙冲淤模型采用平衡挟沙的原理进行计算,希望能提出一个合理有效的计算模型。与此同时,采用二维迎风有限元方法解决二维水流泥沙问题,用三角形网格对计算区域进行剖分,同时为了节省计算机内存,采用集中质量法进行计算。
在建立模型过程中,对于模型方程中有关物理量的确定,在以往研究的基础上又进行了进一步的改进,对前人的工作进行了发展与延伸,同时对海床稳定性条件进行了研究,给出了床面处于不冲不淤的稳定平衡状态的条件,对海床的稳定性判别给出了一个较为具体的判定条件。
最后,为了对所建数学模型进行验证,针对所提出的二维水流泥沙数学模型方程,编制计算程序,并将程序运用于福清湾元载码头三期扩建潮流泥沙计算,结合计算结果对工程的布置及规模确定给予适当的建议,并且希望在此研究基础上该模型能够对粉沙淤泥质海岸泥沙运动特性研究有所帮助,特别是针对于潮流动力作用很强的粉沙淤泥质海岸河口。
This paper is based on the problem that how to construct port structure on silty mud coast which is a very difficult and hot problem at present. A definition to silty mud coast and a new method on research are given, at the same time the characteristics of sediment transport based on the theories that are wildly accepted is analysised.
It is necessary to consider the feature of sediment transport in the port engineering construction, and in this paper a set of the flow-sediment equations which is based the properties of sediment transport on the silty mud coast are established. By the same way, the suspended load and traction load equations and bed surface deformation equation are established.Balance sediment-carrying principle is used in order to give a reasonable calculation model. Meanwhile, two-dimension upwind finite element is used to solve the flow-sediment calculation, and the grid is triangular grid. Lumped mass method is used to saves computer memory.
During the course of modeling building, a further improvement on the physical quantities that are furthermore development and extension based on the previous works is given in this paper. The stability condition of sea bed is studied and a equilibrium condition which provides the judgement of seabed stability is offered.
Finally, in order to test the model, program based on the flow-sediment equations is written and applied.In this paper proper suggestions is given on the construction of ports.It is hoped that the conclusion will be useful in the future research of silty mud coast especially in the research on the coast and estuary where the influence of tide is stronger than wave.
引文
[1]曹祖德,杨树森,杨华,粉沙质海岸的界定及其泥沙运动特点,水运工程,2003,352(5):1-5.
[2]钱宁,万兆惠,泥沙运动力学,北京,科学出版社,1983,39-40.
[3]曹祖德,焦桂英,赵冲久,粉砂质海岸泥沙运动和淤积分析计算,海洋工程,2004,22(1):59-65.
[4]韩西军,粉沙质海岸泥沙淤积的研究,第8届天津市水利学会学术研讨会文集,1996,1—9.
[5]张庆河,徐宏明,秦崇仁等,粉沙质海岸界定浅说和粉沙的基本特性研究,第九届全国海岸工程学术讨论会论文集,北京:海洋出版社,1999,252—258.
[6]曹祖德,我国海岸泥沙运动数值模拟,严恺主编,海岸工程,北京,海洋出版社,2001,665—666.
[7]杨华,赵冲久,侯志强等,粉沙质海岸波浪和潮流作用下泥沙垂线分布研究,水道港口,2006,27(3):142-146.
[8]徐宏明,张庆河,粉沙质海岸泥沙特性实验研究,泥沙研究,2006,(3):42-49.
[9]赵冲久,刘富强,曹祖德,粉沙质海岸泥沙运动特点的实验研究,水道港口,2002,23(4):259-262.
[10]刘家驹,张镜潮,泥质海岸航道、港池淤积计算方法及其推广应用,水利水运科学研究, 1993, (4) :301-320.
[11]罗肇森,河口航道开挖后的回淤计算,泥沙研究, 1987,(2) : 13-20.
[12]曹祖德,泥质海港防沙堤合理长度的确定,水道港口,1993, 12 (3) : 23-27.
[13]庄克琳,李广雪,海岸演化数值模拟研究进展,海洋地质动态,1999,(2):1-3.
[14]刘家驹,粉沙淤泥质海岸的航道淤积,利水运工程学报,2004,(1):6-11.
[15]许国辉,刘德辅,贾同彬,粉砂淤泥质海岸开敞航道淤积模式探讨,海岸工程,2005,24(4):11-16.
[16]赵冲久,黄明政,粉沙质海岸港口外航道淤积物粒径组成的预报方法研究,2007,28(1):1-4.
[17]赵冲久,秦崇仁,杨华等,波流共同作用下粉沙质悬移质运动规律的研究,水道港口,2003,24(3):101-108.
[18]曹祖德,焦桂英,粉沙质海岸泥沙运动推悬比的确定,水道港口,2002,23(1):12-16.
[19]罗刚,杨希宏,粉沙质海岸港口口门位置的选择,中国港湾建设, 2003, (3) : 10-14.
[20]孔令双,曹祖德,李炎保,粉沙质海岸建港的若干泥沙问题,中国港湾建设, 2004, (3) : 24-27.
[21]杨华,麦苗,粉沙质海岸建港的新模式,水道港口,2004,25 (1) : 7-10.
[22]韩西军,曹祖德,杨树森,粉砂质海床上建筑物周围局部冲刷的系列模型延伸法研究,海洋学报,2007,29(1):150-154.
[23]付典龙,傅春,一维圣维南方程组的特征线法,南昌大学学报,2006,28(4):386-389.
[24]吴相忠,张庆河,张娜等,黄骅港海域三维流场数值模拟,水利水运工程学报,2005,(3):13-19.
[25]于风香,宋志尧,李瑞杰,长江口三维潮流数值计算及动力分析,海洋湖沼通报,2003,(3):14-23.
[26]白玉川,海岸三维潮流数学模型的研究,海洋学报,1998,20(6):87-100.
[27]白玉川,于天一,分步分层拟三维水流数学模型及其在廉州湾潮流计算中的应用,海洋学报,1998,20(5):126-135.
[28]董文军,李世森,白玉川,三维潮流和潮流输沙问题的一种混合数值模拟及其应用,海洋学报,1999,21(2):108-114.
[29]Leendertse,JJ.,Water quality model for well-mixed estuary and coastal seas,Vol.1,Princeples of computation.Corp.Santa Monica,Calif.RM-6230-Rc,1970.
[30]Butler,H.S.,A Storm Surge Modedl Study,Vol.Ⅱ,A finite element storm surge analysis and its application to a bay-ocean system,Virgina Inst.Marina Science,Gloucester Point Va.,Spec.Rep.P189,1978.
[31]Dufort,E.C.and Frankel,S.P.,Stability Conditions in the Numerical Treatment of Parabolic Differential Equations,Math Tables and Other Aids to Computation Vol.7,P135-152,1953.
[32]Peaceman,D.W.,Rachford,H.H.,J.Soc.Indus.Appl.Math.3,P28-41,1955.
[33]Douglas,J.Jr.,On the numerical integration of by implicit methods,J.Soc.Indu.Appl.Math.Vol.3,No.1,P42-65,1955
[34]Yanenko,N.N.,The Method of Fractional Steps,Springer-Verleg,Berlin & New York,1971
[35]刘万利,余明辉,陈立,平面二维全沙数值模拟方法及其应用,武汉大学学报,2004,37(6):27-31.
[36]吴江航,韩庆书,计算流体力学理论方法及应用,北京,科学出版社,1988,172-177.
[37]Rayleigh,J.W.S.,Theory of Sound,1 st edn revised,Dover Publications Inc.,New York,P1877,1945
[38]Rita,W.,Uber Eine Neue Mwethods zur Losung Gewisser Variations-probleme der Mathematics chen Phyisk,J.Reine Angew Math,135,No.1,P1,1909
[39]Galerkin,B.G.,Rods and Platers,Series Occurring in Various Questions Concerning the Elastic Equilibrium of Rods and Plates(in Russian),Vestn Inghenvov,19,P897-908,1915
[40]韦直林,河道水流泥沙问题的一种有限元解法,武汉水利电力学院院报,1990,(6):77—86.
[41]白玉川,顾元棪，邢焕政，水流泥沙数学腜屠砺奂坝τ茫旖颍旖?大学出版社,2005,225.
[42]王世澎,梁书秀,孙昭晨,二维情况下波浪对潮流场作用的数值分析,海洋学报,2007,29(2):173-177.
[43]刘万利,河床变形计算方法的研究及其工程应用,水道港口,2004,25(4):185-190.
[44]远航,于定勇,潮流与泥沙数值模拟回顾与进展,海洋科学进展,2004,22(1):97-106.
[45]季则舟,粉沙质海岸港口水域平面布局特点,海洋工程,2006,24(4):81-85.
[46]张庆河,张金凤,杨华等,粉沙质海岸港口布置模式探讨,中国港湾建设,2005,134(1):6-8.
[47]曹祖德,孔令双,李炎保,粉沙质海岸的工程泥沙问题,水道港口,2004,(25):26-30.
[2]钱宁,万兆惠,泥沙运动力学,北京,科学出版社,1983,39-40.
[3]曹祖德,焦桂英,赵冲久,粉砂质海岸泥沙运动和淤积分析计算,海洋工程,2004,22(1):59-65.
[4]韩西军,粉沙质海岸泥沙淤积的研究,第8届天津市水利学会学术研讨会文集,1996,1—9.
[5]张庆河,徐宏明,秦崇仁等,粉沙质海岸界定浅说和粉沙的基本特性研究,第九届全国海岸工程学术讨论会论文集,北京:海洋出版社,1999,252—258.
[6]曹祖德,我国海岸泥沙运动数值模拟,严恺主编,海岸工程,北京,海洋出版社,2001,665—666.
[7]杨华,赵冲久,侯志强等,粉沙质海岸波浪和潮流作用下泥沙垂线分布研究,水道港口,2006,27(3):142-146.
[8]徐宏明,张庆河,粉沙质海岸泥沙特性实验研究,泥沙研究,2006,(3):42-49.
[9]赵冲久,刘富强,曹祖德,粉沙质海岸泥沙运动特点的实验研究,水道港口,2002,23(4):259-262.
[10]刘家驹,张镜潮,泥质海岸航道、港池淤积计算方法及其推广应用,水利水运科学研究, 1993, (4) :301-320.
[11]罗肇森,河口航道开挖后的回淤计算,泥沙研究, 1987,(2) : 13-20.
[12]曹祖德,泥质海港防沙堤合理长度的确定,水道港口,1993, 12 (3) : 23-27.
[13]庄克琳,李广雪,海岸演化数值模拟研究进展,海洋地质动态,1999,(2):1-3.
[14]刘家驹,粉沙淤泥质海岸的航道淤积,利水运工程学报,2004,(1):6-11.
[15]许国辉,刘德辅,贾同彬,粉砂淤泥质海岸开敞航道淤积模式探讨,海岸工程,2005,24(4):11-16.
[16]赵冲久,黄明政,粉沙质海岸港口外航道淤积物粒径组成的预报方法研究,2007,28(1):1-4.
[17]赵冲久,秦崇仁,杨华等,波流共同作用下粉沙质悬移质运动规律的研究,水道港口,2003,24(3):101-108.
[18]曹祖德,焦桂英,粉沙质海岸泥沙运动推悬比的确定,水道港口,2002,23(1):12-16.
[19]罗刚,杨希宏,粉沙质海岸港口口门位置的选择,中国港湾建设, 2003, (3) : 10-14.
[20]孔令双,曹祖德,李炎保,粉沙质海岸建港的若干泥沙问题,中国港湾建设, 2004, (3) : 24-27.
[21]杨华,麦苗,粉沙质海岸建港的新模式,水道港口,2004,25 (1) : 7-10.
[22]韩西军,曹祖德,杨树森,粉砂质海床上建筑物周围局部冲刷的系列模型延伸法研究,海洋学报,2007,29(1):150-154.
[23]付典龙,傅春,一维圣维南方程组的特征线法,南昌大学学报,2006,28(4):386-389.
[24]吴相忠,张庆河,张娜等,黄骅港海域三维流场数值模拟,水利水运工程学报,2005,(3):13-19.
[25]于风香,宋志尧,李瑞杰,长江口三维潮流数值计算及动力分析,海洋湖沼通报,2003,(3):14-23.
[26]白玉川,海岸三维潮流数学模型的研究,海洋学报,1998,20(6):87-100.
[27]白玉川,于天一,分步分层拟三维水流数学模型及其在廉州湾潮流计算中的应用,海洋学报,1998,20(5):126-135.
[28]董文军,李世森,白玉川,三维潮流和潮流输沙问题的一种混合数值模拟及其应用,海洋学报,1999,21(2):108-114.
[29]Leendertse,JJ.,Water quality model for well-mixed estuary and coastal seas,Vol.1,Princeples of computation.Corp.Santa Monica,Calif.RM-6230-Rc,1970.
[30]Butler,H.S.,A Storm Surge Modedl Study,Vol.Ⅱ,A finite element storm surge analysis and its application to a bay-ocean system,Virgina Inst.Marina Science,Gloucester Point Va.,Spec.Rep.P189,1978.
[31]Dufort,E.C.and Frankel,S.P.,Stability Conditions in the Numerical Treatment of Parabolic Differential Equations,Math Tables and Other Aids to Computation Vol.7,P135-152,1953.
[32]Peaceman,D.W.,Rachford,H.H.,J.Soc.Indus.Appl.Math.3,P28-41,1955.
[33]Douglas,J.Jr.,On the numerical integration of by implicit methods,J.Soc.Indu.Appl.Math.Vol.3,No.1,P42-65,1955
[34]Yanenko,N.N.,The Method of Fractional Steps,Springer-Verleg,Berlin & New York,1971
[35]刘万利,余明辉,陈立,平面二维全沙数值模拟方法及其应用,武汉大学学报,2004,37(6):27-31.
[36]吴江航,韩庆书,计算流体力学理论方法及应用,北京,科学出版社,1988,172-177.
[37]Rayleigh,J.W.S.,Theory of Sound,1 st edn revised,Dover Publications Inc.,New York,P1877,1945
[38]Rita,W.,Uber Eine Neue Mwethods zur Losung Gewisser Variations-probleme der Mathematics chen Phyisk,J.Reine Angew Math,135,No.1,P1,1909
[39]Galerkin,B.G.,Rods and Platers,Series Occurring in Various Questions Concerning the Elastic Equilibrium of Rods and Plates(in Russian),Vestn Inghenvov,19,P897-908,1915
[40]韦直林,河道水流泥沙问题的一种有限元解法,武汉水利电力学院院报,1990,(6):77—86.
[41]白玉川,顾元棪，邢焕政，水流泥沙数学腜屠砺奂坝τ茫旖颍旖?大学出版社,2005,225.
[42]王世澎,梁书秀,孙昭晨,二维情况下波浪对潮流场作用的数值分析,海洋学报,2007,29(2):173-177.
[43]刘万利,河床变形计算方法的研究及其工程应用,水道港口,2004,25(4):185-190.
[44]远航,于定勇,潮流与泥沙数值模拟回顾与进展,海洋科学进展,2004,22(1):97-106.
[45]季则舟,粉沙质海岸港口水域平面布局特点,海洋工程,2006,24(4):81-85.
[46]张庆河,张金凤,杨华等,粉沙质海岸港口布置模式探讨,中国港湾建设,2005,134(1):6-8.
[47]曹祖德,孔令双,李炎保,粉沙质海岸的工程泥沙问题,水道港口,2004,(25):26-30.