波、流联合作用下二维水流、泥沙数学模型研究
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摘要
淤泥质海岸泥沙的淤积问题一直是困绕港口、航道正常作业的关键问题。二维水流泥沙数学模型是计算航道和港内泥沙淤积量的有效方法,本文拟对此开展研究。主要研究工作概括如下。
一、用COASTTOOL2D水流模型进行流场模拟,并对模型进行了改进。在数值模拟中发现,原COASTTOOL2D水流模型在底坡较大时通量计算会产生较大误差。其原因是在非线性通量计算中近似采用了单元边平均水深,本文通过积分导出了倾斜底坡下对流通量的补偿项,从而使模型可推广到地形变化较大的区域。
二、在动边界处理中,新提出一种网格淹没度的概念,并据此导出一种控制方程新的离散方法,将半淹没网格视为渐变连续体处理,使边界处水量计算与动边界实际位置相吻合。应用此种方法可以将动边界单元与内单元统一处理,从而避免了动边界处因干湿单元变换引起的数值振荡。此方法的特点是在无须重新划分网格前提下达到可变网格的计算效果,理论上严谨,应用方便,计算准确且速度较快,在工程中有很强的实用性。
三、新提出一种线单元处理方法,用于模拟水下强变化地形——潜堤。数值实验表明,潜堤淹没前后,流场可以平顺过度,增强了模型的适应性。
四、在水流和泥沙模型中考虑波浪的影响,建立了波流共同作用下悬沙输运数学模型,运用该模型对天津港及其周围海区泥沙运动过程进行了模拟。
Sediment siltation has always been a big problem that affects the normal operation of ports and channels on muddy coast. 2D sediment numerical model is an efficient method to calculate the sediment deposition in the harbor and channel. In this dissertation some research will be carried out on this topic and is outlined as follows.
1. Numerical simulations will be performed by using the COASTTOOL2D flow model to study the flow field, and then the model will be improved by means of theoretical analysis and strict derivation. In the numerical tests of flow field it is found that the former version of the COASTTOOL2D flow model involves significant error in the calculation of numerical flux under the condition of a steep bottom slope. The reason for the error is that the average water depth on each side of the grid is adopted when calculating the nonlinear numerical flux. In this research, a compensation term for the convective flux, which is caused by the bottom slope of the element side, is derived by means of integration and is added to the discretized equation. In this way, the COASTTOOL2D flow model can be extended to the areas where topography varies violently.
2. In the treatment of movable boundary, we put forward a new discretization method for the governing equations according to a newly proposed concept——submergence index. By this method, the semi-submerged elements can transit smoothly and continuously from a dry one to a completely wet one instead of an abrupt shift, which makes it is possible to adjust the water quantity exactly according to the location of the movable boundary and to implement a unified approach in dealing with the elements at movable boundary and inner grids. It is also possible that numerical oscillation caused by abrupt shift between wet and dry elements can be avoided. The advantages of the method are that not only can we obtain a higher computational efficiency of variable element without reconstruction of element system, it is also strict in theory, convenient for application, accurate in calculation and with a high processing speed. The improved COASTTOOL2D flow model can be widely used in practical engineering.
3. In the thesis, a new concept of line element is proposed, on the basis of which, the model is improved for the application of flow over a violently varying underwater topography, e.g. a submerged dike. Numerical tests indicate the success of the model to be applicable to the case of submerged dike and thus the application range of the model is further extended.
4. In the flow and sediment model we incorporate the effect of wave effect. And by using the model, tide flow and sediment movement inside and around Tianjin Port are simulated.
一、用COASTTOOL2D水流模型进行流场模拟,并对模型进行了改进。在数值模拟中发现,原COASTTOOL2D水流模型在底坡较大时通量计算会产生较大误差。其原因是在非线性通量计算中近似采用了单元边平均水深,本文通过积分导出了倾斜底坡下对流通量的补偿项,从而使模型可推广到地形变化较大的区域。
二、在动边界处理中,新提出一种网格淹没度的概念,并据此导出一种控制方程新的离散方法,将半淹没网格视为渐变连续体处理,使边界处水量计算与动边界实际位置相吻合。应用此种方法可以将动边界单元与内单元统一处理,从而避免了动边界处因干湿单元变换引起的数值振荡。此方法的特点是在无须重新划分网格前提下达到可变网格的计算效果,理论上严谨,应用方便,计算准确且速度较快,在工程中有很强的实用性。
三、新提出一种线单元处理方法,用于模拟水下强变化地形——潜堤。数值实验表明,潜堤淹没前后,流场可以平顺过度,增强了模型的适应性。
四、在水流和泥沙模型中考虑波浪的影响,建立了波流共同作用下悬沙输运数学模型,运用该模型对天津港及其周围海区泥沙运动过程进行了模拟。
Sediment siltation has always been a big problem that affects the normal operation of ports and channels on muddy coast. 2D sediment numerical model is an efficient method to calculate the sediment deposition in the harbor and channel. In this dissertation some research will be carried out on this topic and is outlined as follows.
1. Numerical simulations will be performed by using the COASTTOOL2D flow model to study the flow field, and then the model will be improved by means of theoretical analysis and strict derivation. In the numerical tests of flow field it is found that the former version of the COASTTOOL2D flow model involves significant error in the calculation of numerical flux under the condition of a steep bottom slope. The reason for the error is that the average water depth on each side of the grid is adopted when calculating the nonlinear numerical flux. In this research, a compensation term for the convective flux, which is caused by the bottom slope of the element side, is derived by means of integration and is added to the discretized equation. In this way, the COASTTOOL2D flow model can be extended to the areas where topography varies violently.
2. In the treatment of movable boundary, we put forward a new discretization method for the governing equations according to a newly proposed concept——submergence index. By this method, the semi-submerged elements can transit smoothly and continuously from a dry one to a completely wet one instead of an abrupt shift, which makes it is possible to adjust the water quantity exactly according to the location of the movable boundary and to implement a unified approach in dealing with the elements at movable boundary and inner grids. It is also possible that numerical oscillation caused by abrupt shift between wet and dry elements can be avoided. The advantages of the method are that not only can we obtain a higher computational efficiency of variable element without reconstruction of element system, it is also strict in theory, convenient for application, accurate in calculation and with a high processing speed. The improved COASTTOOL2D flow model can be widely used in practical engineering.
3. In the thesis, a new concept of line element is proposed, on the basis of which, the model is improved for the application of flow over a violently varying underwater topography, e.g. a submerged dike. Numerical tests indicate the success of the model to be applicable to the case of submerged dike and thus the application range of the model is further extended.
4. In the flow and sediment model we incorporate the effect of wave effect. And by using the model, tide flow and sediment movement inside and around Tianjin Port are simulated.
引文
[1]李孟国,曹祖德,海岸河口潮流数值模拟的研究与进展,海洋学报,1999,21(1):111~125
[2]Leendertse J J. Aspects of a computational model for long-period water-wave propagation. The Rand Corporation, 1967
[3]谭维炎,胡四一,二维浅水流动的一种普适的高性能格式,水科学进展,1991,2(3):154~161
[4]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,水科学进展,1994,5(4):262~270
[5]谭维炎,胡四一,无结构网格上二维浅水流动的数值模拟,水科学进展,1995,6(1):1~9
[6]谭维炎,胡四一,韩曾萃等,钱塘江口涌潮二维数值模拟,水科学进展,1995,6(2):83~93
[7]赵棣华,戚晨,庾维德等,平面二维水流-水质有限体积法及黎曼近似解模型,水科学进展,2000,11(4):368~374
[8]潘存鸿,林炳尧,毛献忠,求解二维浅水方程的Godunov格式,水动力学研究与进展,2003,18(1):16~23
[9]Park K, and Kuo, A. Y. A Vertical Two Dimensional Model of Estuarine Hydrodynamics and Water Quality. Special Report in Applied Marine Science and Ocean Engineering, 1992, No.321
[10]时钟,李世森,垂向二维潮流数值模型及其在长江口北槽的应用,海洋通报,2003,22(3):1~8
[11]Leendertse J J. A Three-dimensional Model for Estuaries and Coastal Seas. The Rand Corporation,1973
[12]Backhaus J O. A semi-implicit scheme for the shallow water equations for application to shelf sea modeling. Theoretical or Mathematical,1983.2(4):243~254
[13]Blumberg A F,Mellor G L. A description of a three-dimensional coastal ocean circulation model. Amer Georphys Union,1987.1~16
[14]董文军,河口近岸区三维潮流及悬沙扩散的一种分布模型,天津大学学报,1999,32(3):246~249
[15]白玉川,海岸三维潮流数学模型的研究及应用,海洋学报,1998,20(6):97~100
[16]朱志夏,波浪、潮流联合作用下泥沙数学模型的理论研究及其应用,[博士学位论文],天津大学,1997
[17]陈景仁,湍流模型及有限分析法,上海:上海交通大学出版社,1989
[18]谭维炎,计算浅水动力学——有限体积法的应用,北京:清华大学出版社,1998
[19]Changsheng Chen, Hedong Liu. An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries. Journal of atmospheric and oceanic technology,2003.20:159~186
[20]曹祖德,王桂芬,波浪掀沙、潮流输沙的数值模拟,海洋学报,1993,15(1)
[21]窦国仁,董凤舞,窦希萍,河口海岸泥沙数学模型研究,中国科学(A辑),1995,25(9):995~1001
[22]辛文杰,潮流、波浪综合作用下河口二维悬沙数学模型,海洋工程,1997,15(2):30~47
[23]马福喜、李文新,河口水流、波浪、潮流、泥沙、河床变形二维数学模型,水利学报,1999,5:39~43
[24]李大鸣、白志刚、朱志夏,波流联合作用下海床演变的长期预报泥沙数学模型,中国港湾建设,1999,5:33~40
[25]白玉川,顾元棪，蒋昌波，潮流波浪联合输沙及?渤逵傺荼涞睦砺厶逑涤?其数学模拟,海洋与湖沼,2000,31(2):186~196
[26]丁平兴,胡克林,孔亚珍,长江河口波-流共同作用下的全沙数值模拟,海洋学报,2003,25(5):113~124
[27]窦国仁、董风舞、Xiping Dou,波浪和潮流的挟沙能力,科学通报,1995,40(5):443~446
[28]曹文洪,张启舜,潮流和波浪作用下悬移质挟沙能力的研究,泥沙研究,2000,5:16~21
[29]孙健,陶建华,潮流数值模拟中动边界处理方法研究,水动力学研究与进展,2007,A22(1):44~52
[30]张世奇,二维动边界潮流输沙及河床变形计算,泥沙研究,1988,4:55~63
[31]彭凯,方铎,曹叔尤,在二维流动计算中应用“河床切削”技术处理动边界问题,水动力学研究与进展,1992,A7(2):200~205
[32]潘存鸿,林炳尧,毛放忠,浅水问题动边界数值模拟,水利水运工程学报,2004,4:1~7
[33]朱德军,陈永灿,刘昭伟,处理二维浅水流动中动边界问题的淹没节点法,水动力学研究与进展,2006,A21(1):102~106
[34]张玉东,纪楚群,包含动边界的非定常流场动网格数值模拟,计算物理,2006,23(2):165~170
[35]申霞,姚琪,王鹏,动边界技术在POM模型中的研究与应用,海洋通报,2006,25(1):1~7
[36]张军,谭俊杰,任登凤,二维含动边界流场的并行计算,河海大学学报(自然科学版),2007,35(4):460~463
[37]李绍武,卢丽锋,时钟,河口准三维涌潮数学模型研究,水动力学研究与进展,2004,A19(4):407~415
[38]李绍武,郑建军,回流区水流运动二维数值模拟,港工技术,2004,4:8~10
[39]郑建军,非结构三角形网格下三维浅水流动的数值模拟:[硕士学位论文],天津;天津大学,2006
[40]王建军,一种有限体积法三维水流悬沙数学模型研究,[硕士学位论文],天津;天津大学,2007
[41]黄泰坤,波、流共同作用下三维泥沙运动数值模型研究,[硕士学位论文],天津;天津大学,2007
[42]李孟国,海岸河口泥沙数学模型研究进展,海洋工程,2006,24(1):139~154
[43]曹祖德,李蓓,孔令双,波、流共存时的水体挟沙力,水道港口,2001,22(4)151~155
[44]吴宋仁主编,海岸动力学,北京:人民交通出版社,1999,46~58
[45]Yoshimi Goda. Random Seas and Design of Maritime Structures. University of Tokyo press, 1985.71~74
[46]张庆河,侯凤林,夏波等,黄骅港外航道淤积的二维数学模拟,中国港湾建设,2006,5:6~9
[47]J?rgen Freds?e, Rolf Deigaard. Mechanics of Coastal Sediment Transport, Singapore: World Scientific, 1992.89~94
[2]Leendertse J J. Aspects of a computational model for long-period water-wave propagation. The Rand Corporation, 1967
[3]谭维炎,胡四一,二维浅水流动的一种普适的高性能格式,水科学进展,1991,2(3):154~161
[4]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,水科学进展,1994,5(4):262~270
[5]谭维炎,胡四一,无结构网格上二维浅水流动的数值模拟,水科学进展,1995,6(1):1~9
[6]谭维炎,胡四一,韩曾萃等,钱塘江口涌潮二维数值模拟,水科学进展,1995,6(2):83~93
[7]赵棣华,戚晨,庾维德等,平面二维水流-水质有限体积法及黎曼近似解模型,水科学进展,2000,11(4):368~374
[8]潘存鸿,林炳尧,毛献忠,求解二维浅水方程的Godunov格式,水动力学研究与进展,2003,18(1):16~23
[9]Park K, and Kuo, A. Y. A Vertical Two Dimensional Model of Estuarine Hydrodynamics and Water Quality. Special Report in Applied Marine Science and Ocean Engineering, 1992, No.321
[10]时钟,李世森,垂向二维潮流数值模型及其在长江口北槽的应用,海洋通报,2003,22(3):1~8
[11]Leendertse J J. A Three-dimensional Model for Estuaries and Coastal Seas. The Rand Corporation,1973
[12]Backhaus J O. A semi-implicit scheme for the shallow water equations for application to shelf sea modeling. Theoretical or Mathematical,1983.2(4):243~254
[13]Blumberg A F,Mellor G L. A description of a three-dimensional coastal ocean circulation model. Amer Georphys Union,1987.1~16
[14]董文军,河口近岸区三维潮流及悬沙扩散的一种分布模型,天津大学学报,1999,32(3):246~249
[15]白玉川,海岸三维潮流数学模型的研究及应用,海洋学报,1998,20(6):97~100
[16]朱志夏,波浪、潮流联合作用下泥沙数学模型的理论研究及其应用,[博士学位论文],天津大学,1997
[17]陈景仁,湍流模型及有限分析法,上海:上海交通大学出版社,1989
[18]谭维炎,计算浅水动力学——有限体积法的应用,北京:清华大学出版社,1998
[19]Changsheng Chen, Hedong Liu. An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries. Journal of atmospheric and oceanic technology,2003.20:159~186
[20]曹祖德,王桂芬,波浪掀沙、潮流输沙的数值模拟,海洋学报,1993,15(1)
[21]窦国仁,董凤舞,窦希萍,河口海岸泥沙数学模型研究,中国科学(A辑),1995,25(9):995~1001
[22]辛文杰,潮流、波浪综合作用下河口二维悬沙数学模型,海洋工程,1997,15(2):30~47
[23]马福喜、李文新,河口水流、波浪、潮流、泥沙、河床变形二维数学模型,水利学报,1999,5:39~43
[24]李大鸣、白志刚、朱志夏,波流联合作用下海床演变的长期预报泥沙数学模型,中国港湾建设,1999,5:33~40
[25]白玉川,顾元棪，蒋昌波，潮流波浪联合输沙及?渤逵傺荼涞睦砺厶逑涤?其数学模拟,海洋与湖沼,2000,31(2):186~196
[26]丁平兴,胡克林,孔亚珍,长江河口波-流共同作用下的全沙数值模拟,海洋学报,2003,25(5):113~124
[27]窦国仁、董风舞、Xiping Dou,波浪和潮流的挟沙能力,科学通报,1995,40(5):443~446
[28]曹文洪,张启舜,潮流和波浪作用下悬移质挟沙能力的研究,泥沙研究,2000,5:16~21
[29]孙健,陶建华,潮流数值模拟中动边界处理方法研究,水动力学研究与进展,2007,A22(1):44~52
[30]张世奇,二维动边界潮流输沙及河床变形计算,泥沙研究,1988,4:55~63
[31]彭凯,方铎,曹叔尤,在二维流动计算中应用“河床切削”技术处理动边界问题,水动力学研究与进展,1992,A7(2):200~205
[32]潘存鸿,林炳尧,毛放忠,浅水问题动边界数值模拟,水利水运工程学报,2004,4:1~7
[33]朱德军,陈永灿,刘昭伟,处理二维浅水流动中动边界问题的淹没节点法,水动力学研究与进展,2006,A21(1):102~106
[34]张玉东,纪楚群,包含动边界的非定常流场动网格数值模拟,计算物理,2006,23(2):165~170
[35]申霞,姚琪,王鹏,动边界技术在POM模型中的研究与应用,海洋通报,2006,25(1):1~7
[36]张军,谭俊杰,任登凤,二维含动边界流场的并行计算,河海大学学报(自然科学版),2007,35(4):460~463
[37]李绍武,卢丽锋,时钟,河口准三维涌潮数学模型研究,水动力学研究与进展,2004,A19(4):407~415
[38]李绍武,郑建军,回流区水流运动二维数值模拟,港工技术,2004,4:8~10
[39]郑建军,非结构三角形网格下三维浅水流动的数值模拟:[硕士学位论文],天津;天津大学,2006
[40]王建军,一种有限体积法三维水流悬沙数学模型研究,[硕士学位论文],天津;天津大学,2007
[41]黄泰坤,波、流共同作用下三维泥沙运动数值模型研究,[硕士学位论文],天津;天津大学,2007
[42]李孟国,海岸河口泥沙数学模型研究进展,海洋工程,2006,24(1):139~154
[43]曹祖德,李蓓,孔令双,波、流共存时的水体挟沙力,水道港口,2001,22(4)151~155
[44]吴宋仁主编,海岸动力学,北京:人民交通出版社,1999,46~58
[45]Yoshimi Goda. Random Seas and Design of Maritime Structures. University of Tokyo press, 1985.71~74
[46]张庆河,侯凤林,夏波等,黄骅港外航道淤积的二维数学模拟,中国港湾建设,2006,5:6~9
[47]J?rgen Freds?e, Rolf Deigaard. Mechanics of Coastal Sediment Transport, Singapore: World Scientific, 1992.89~94