淹没丁坝对水流结构的调整作用研究
|
摘要
工程实践中淹没丁坝是很常见的工况,不同淹没程度△H／H下丁坝对水流结构的调整作用是不同的。实际应用的丁坝具有迎水边坡、背水边坡和端坡,与水槽试验中常见的直立丁坝也有很大不同。采用水槽试验和三维数学模型相结合的方法,主要研究具有迎水边坡和背水边坡的丁坝在非淹没和△H／H=0.17、0.29、0.38和0.44时和相同阻挡面积下端坡系数m=0、3、5和7时水流结构的变化。
1)建立基于平面三角形网格和垂向σ坐标系的三维Roe格式浅水紊流模型。推导出σ坐标系下守恒扩散模型。采用计算糙率、水位积分平衡法、三维阶梯流水力模型和部分滑移系数处理丁坝水流模拟中的三维动边界、陡坡、高程间断和边壁阻力问题。考虑边壁阻力的影响能够模拟出非淹没丁坝上、下游小回流区。
2)△H／H=0.17时,丁坝下游仍出现回流区；△H／H>0.17时,回流区消失。淹没时坝头附近横向流速较非淹没时减弱,下游回流区内纵向流速分布较非淹没时更为均匀。在受坝体阻挡的纵剖面上,淹没时坝顶的表层纵向流速为1.1～1.7V0(V0为平均流速),在下游出现横轴环流。
淹没丁坝对低于坝顶的水流仍起一定的调整作用,这种作用随着△H／H的增加而减弱。坝顶以上和坝头附近的流向偏角和横向流速随着△H／H的增加而减小。m=0时横向水流影响范围bt／L与△H／H呈如下经验关系：bt/L=-5.80△H/H+2.96。
3)推导出非淹没和淹没时不同m下丁坝阻挡流量计算公式。考虑端坡对局部水头损失的影响建立非淹没时下游回流区长度计算公式；结合坝顶过流对坝轴断面主流区平均流速的影响建立△H／H较小时丁坝下游回流区长度公式。
非淹没时m的增加引起相对回流长度l／L和相对回流宽度b／L的减小。底层平面相对流速V/V0≥1.40和相对底床切应力τb/τb0≥3.00等值线范围随着m的增加明显减小,最大相对底床切应力τbmax／τ0由m=0时的4.40减小至m=7时的3.68。
△H／H=0.17时,l/L从m=0时的7.81增至m=1时的9.56,然后随m增加逐渐减小至m=7时为8.16。这种变化趋势与非淹没时的不同。底层平面V／V0≥1.30和τb／τb0≥2.50等值线范围随着m的增加而减小。τbmax/τ0至m=7时已基本稳定为2.90。
4)m=0时坝轴断面相对单宽流量q/qin在坝头处明显集中,随着m增大至7时逐渐减小至1.18并与主流区中的趋于一致。坝头从直立到m=3时,端坡的调整作用体现在q/qin=1.35等值线内强度的降低上,但等值线范围未有较大增加甚至缩小。当m>3时,端坡的调整作用体现在q/qin≥1.15等值线范围的减小上。
△H／H的增加使得坝顶q/qin增加和主流区q/qin减小,丁坝对水流的调节作用减弱,单宽流量的分布趋于均匀。
5)存在端坡时,底层平面V/V0≥1.30和τb/τb0≥2.50等值线范围、τbmax/τb0和q／qin的集中程度等都比坝头直立时大为缩小。另外,端坡的存使得下沉水流和漩涡系不能直接作用于坝头的河床。这些对限制坝头局部冲刷和将更多的流量分配到主流区都是有利的。
In projects, especially channel improvement, submerged spur dikes have been widely used. The impact of spur dike on flow structure has changed with overtopping ratio. Spur dikes in engineering normally have upstream slope, downstream slope and head slope, which lead to great difference compared to vertical-wall ones. Flume experiment and 3D mathematical model are used together to study on the impact of head slope coefficient m=0,3,5 and 7 and overtopping ratio△H/H=0.17,0.29,0.38 and 0.44 on local flow structure.
1) A 3D shallow water turbulence model with Roe flux format has been established, based on plane unstructured triangle grid and verticalσcoordinate. A conservative diffusion model has been deduced. Computational roughness, water level integral balance method,3D cascade flow hydraulic model and partial slip coefficient are used to solve problems of 3D movable boundary, steep topography, discontinuous elevation and side wall friction simulation, respectively. Consideration of side wall friction is crucial to simulate two small recirculation zones at upstream and downstream near the root of spur dike.
2) Downstream recirculation zone has also existed in condition of△H/H=0.17, and disappeared in condition of△H/H>0.17. Transverse flow velocity near spur tip is weaker in submerged condition than in non-submerged condition. In section blocked by submerged spur dike, surface longitudinal velocity is 1.1～1.7V0 (mean velocity), and a downstream horizontal axis circulation occurs.
Submerged spur dike has also had adjustment effect in some extent on flow lower than crest, decreasing with increase of△H/H. Deflection angle and transverse flow velocity above crest and next to spur tip have decreased with increase of△H/H. In condition of m=0, a empirical formula between influence extension of transverse flow bt/L and△H/H is as follows:bt/L=-5.80△H/H+2.96.
3) A formula has been deduced to compute discharge blocked by spur dike with m in condition of submerged and non-submerged. In consideration of impact of head slope on local head loss, a formula has been proposed to compute downstream recirculation length in condition of non-submerged. And together with impact of overtopping flow on mean velocity in main flume of spur dike axis section, the similar formula has been proposed for small△H/H.
In condition of non-submerged, the increase of m has lead to decrease of relative recirculation length l/L and relative recirculation width b/L. The isoline extensions of relative plane velocity V/V0≥1.40 near river bed and relative river bed shear stress have both obviously decreased. The maximum of relative river bed shear stressτbmax/τ0 has decreased from 4.40 at m=0 to 3.68 at m=7.
In condition of△H/H=0.17, l/L has increased form 7.81 at m=0 to 9.56 at m=1, and then gradually decreased to 8.16 at m=7, which is different with non-submerged condition. The isoline extensions of river bed plane V/V0≥1.30 andτb/τb0≥2.50 both have decreased with increase of m.τbmax/τ0 has stabilized with 2.90 at m=1.
4) Relative unit-width discharge q/qin in spur dike axis section has significantly concentrated at m=0, and has gradually decreased to 1.18, which equals to that in main flume, at m=7. Adjustment effect of head slope has been shown decrease of intension in isoline of q/qin=1.35 from m=0 to m=3, with not obvious increase, even decrease of isoline extension; and decrease of isoline extension of q/qin=1.15 when m>3.
The increase of△H/H has brought about increase of q/qin above crest and decrease in main flow zone, weakening adjustment effect by spur dike, and unifying distribution of unit-width discharge.
5) The isoline extensions of river bed plane V/V0≥1.30 andτb/τb0≥2.50 and concentration degree ofτbmax/τb0 and q/qin has greatly shrinked with head slope compared to without head slope. In addition, head slope limits down fall flow, and prevents down fall flow and eddy system to directly effect on river bed. All above are beneficial to weaken local scour and transform more discharge to main flume.
1)建立基于平面三角形网格和垂向σ坐标系的三维Roe格式浅水紊流模型。推导出σ坐标系下守恒扩散模型。采用计算糙率、水位积分平衡法、三维阶梯流水力模型和部分滑移系数处理丁坝水流模拟中的三维动边界、陡坡、高程间断和边壁阻力问题。考虑边壁阻力的影响能够模拟出非淹没丁坝上、下游小回流区。
2)△H／H=0.17时,丁坝下游仍出现回流区；△H／H>0.17时,回流区消失。淹没时坝头附近横向流速较非淹没时减弱,下游回流区内纵向流速分布较非淹没时更为均匀。在受坝体阻挡的纵剖面上,淹没时坝顶的表层纵向流速为1.1～1.7V0(V0为平均流速),在下游出现横轴环流。
淹没丁坝对低于坝顶的水流仍起一定的调整作用,这种作用随着△H／H的增加而减弱。坝顶以上和坝头附近的流向偏角和横向流速随着△H／H的增加而减小。m=0时横向水流影响范围bt／L与△H／H呈如下经验关系：bt/L=-5.80△H/H+2.96。
3)推导出非淹没和淹没时不同m下丁坝阻挡流量计算公式。考虑端坡对局部水头损失的影响建立非淹没时下游回流区长度计算公式；结合坝顶过流对坝轴断面主流区平均流速的影响建立△H／H较小时丁坝下游回流区长度公式。
非淹没时m的增加引起相对回流长度l／L和相对回流宽度b／L的减小。底层平面相对流速V/V0≥1.40和相对底床切应力τb/τb0≥3.00等值线范围随着m的增加明显减小,最大相对底床切应力τbmax／τ0由m=0时的4.40减小至m=7时的3.68。
△H／H=0.17时,l/L从m=0时的7.81增至m=1时的9.56,然后随m增加逐渐减小至m=7时为8.16。这种变化趋势与非淹没时的不同。底层平面V／V0≥1.30和τb／τb0≥2.50等值线范围随着m的增加而减小。τbmax/τ0至m=7时已基本稳定为2.90。
4)m=0时坝轴断面相对单宽流量q/qin在坝头处明显集中,随着m增大至7时逐渐减小至1.18并与主流区中的趋于一致。坝头从直立到m=3时,端坡的调整作用体现在q/qin=1.35等值线内强度的降低上,但等值线范围未有较大增加甚至缩小。当m>3时,端坡的调整作用体现在q/qin≥1.15等值线范围的减小上。
△H／H的增加使得坝顶q/qin增加和主流区q/qin减小,丁坝对水流的调节作用减弱,单宽流量的分布趋于均匀。
5)存在端坡时,底层平面V/V0≥1.30和τb/τb0≥2.50等值线范围、τbmax/τb0和q／qin的集中程度等都比坝头直立时大为缩小。另外,端坡的存使得下沉水流和漩涡系不能直接作用于坝头的河床。这些对限制坝头局部冲刷和将更多的流量分配到主流区都是有利的。
In projects, especially channel improvement, submerged spur dikes have been widely used. The impact of spur dike on flow structure has changed with overtopping ratio. Spur dikes in engineering normally have upstream slope, downstream slope and head slope, which lead to great difference compared to vertical-wall ones. Flume experiment and 3D mathematical model are used together to study on the impact of head slope coefficient m=0,3,5 and 7 and overtopping ratio△H/H=0.17,0.29,0.38 and 0.44 on local flow structure.
1) A 3D shallow water turbulence model with Roe flux format has been established, based on plane unstructured triangle grid and verticalσcoordinate. A conservative diffusion model has been deduced. Computational roughness, water level integral balance method,3D cascade flow hydraulic model and partial slip coefficient are used to solve problems of 3D movable boundary, steep topography, discontinuous elevation and side wall friction simulation, respectively. Consideration of side wall friction is crucial to simulate two small recirculation zones at upstream and downstream near the root of spur dike.
2) Downstream recirculation zone has also existed in condition of△H/H=0.17, and disappeared in condition of△H/H>0.17. Transverse flow velocity near spur tip is weaker in submerged condition than in non-submerged condition. In section blocked by submerged spur dike, surface longitudinal velocity is 1.1～1.7V0 (mean velocity), and a downstream horizontal axis circulation occurs.
Submerged spur dike has also had adjustment effect in some extent on flow lower than crest, decreasing with increase of△H/H. Deflection angle and transverse flow velocity above crest and next to spur tip have decreased with increase of△H/H. In condition of m=0, a empirical formula between influence extension of transverse flow bt/L and△H/H is as follows:bt/L=-5.80△H/H+2.96.
3) A formula has been deduced to compute discharge blocked by spur dike with m in condition of submerged and non-submerged. In consideration of impact of head slope on local head loss, a formula has been proposed to compute downstream recirculation length in condition of non-submerged. And together with impact of overtopping flow on mean velocity in main flume of spur dike axis section, the similar formula has been proposed for small△H/H.
In condition of non-submerged, the increase of m has lead to decrease of relative recirculation length l/L and relative recirculation width b/L. The isoline extensions of relative plane velocity V/V0≥1.40 near river bed and relative river bed shear stress have both obviously decreased. The maximum of relative river bed shear stressτbmax/τ0 has decreased from 4.40 at m=0 to 3.68 at m=7.
In condition of△H/H=0.17, l/L has increased form 7.81 at m=0 to 9.56 at m=1, and then gradually decreased to 8.16 at m=7, which is different with non-submerged condition. The isoline extensions of river bed plane V/V0≥1.30 andτb/τb0≥2.50 both have decreased with increase of m.τbmax/τ0 has stabilized with 2.90 at m=1.
4) Relative unit-width discharge q/qin in spur dike axis section has significantly concentrated at m=0, and has gradually decreased to 1.18, which equals to that in main flume, at m=7. Adjustment effect of head slope has been shown decrease of intension in isoline of q/qin=1.35 from m=0 to m=3, with not obvious increase, even decrease of isoline extension; and decrease of isoline extension of q/qin=1.15 when m>3.
The increase of△H/H has brought about increase of q/qin above crest and decrease in main flow zone, weakening adjustment effect by spur dike, and unifying distribution of unit-width discharge.
5) The isoline extensions of river bed plane V/V0≥1.30 andτb/τb0≥2.50 and concentration degree ofτbmax/τb0 and q/qin has greatly shrinked with head slope compared to without head slope. In addition, head slope limits down fall flow, and prevents down fall flow and eddy system to directly effect on river bed. All above are beneficial to weaken local scour and transform more discharge to main flume.
引文
[1]王益良,李旺生.丁坝在航道整治中的应用[J].水道港口,1991,3：40-47.
[2]马颖,江恩惠,李军华,等.丁坝在莱茵河整治中的作用[J].人民长江,2008,39(5)：77-79.
[3]陈志昌,乐嘉钻.长江口深水航道整治原理[J].水利水运工程学报,2005,1：1-7.
[4]窦国仁.窦国仁论文集[C].北京：中国水利水电出版社,2003.260-279.
[5]程年生,李昌华.有边坡丁坝回流试验研究[J].水利水运科学研究,1991,2：123-132.
[6]冯永忠.错口丁坝回流尺度的研究[J].河海大学学报,1995,23(4)：69-76.
[7]乐培九,李旺生,杨细根.丁坝回流长度[J].水道港口,1999,2：3-9.
[8]李国斌,韩信,傅津先.非淹没丁坝下游回流长度及最大回流宽度研究[J].泥沙研究,2001,3：68-73.
[9]孔祥柏,胡美英,吴济难,等.丁坝对水流影响的试验研究[J].水利水运科学研究,1983,68-78.
[10]Lu Y J, Zhou Y T. Flow mechanism and velocity field near groin-like structures [J]. Journal of China Ocean Engineering,1989,3(2):203-216.
[11]应强,孔祥柏.非等长淹没丁坝群局部水头损失的计算[J].水科学进展,1994,5(3)：214-220.
[12]孔祥柏,程年生.丁、潜坝局部水头损失的试验研究[J].水利水运科学研究,1992,4：387-395.
[13]Azinfar H, Kells J A. Backwater effect due to a single spur dike [J]. Can. J. Civ. Eng.,2007, 34:107-115.
[14]Muto Y, Baba Y, Aya S. Velocity measurements in open channel flow with rectangular embayments formed by spur dikes [J]. Annuals of Disas. Prev. Inst.,2002,45(B2):449-457.
[15]Wu B S, Wang G Q, Ma J M, et al. Case study:river training and its effects on fluvial processes in the Lower Yellow River, China [J]. Journal of Hydraulic Engineering,2005, 131(2):85-97.
[16]Anlanger C, Sukhodolov A, Schnauder I, et al. Impact of submerged groynes on the flow field results from a field experiment at the river Spree, Germany [C]. EGU General Assembly,2008, Vienna, Austria. EGU2008-A-11145.
[17]陈稚聪,黑鹏飞,丁翔.丁坝回流区水流紊动强度试验[J].清华大学学报(自然科学版),2008,48(12)：2053-2056.
[18]彭静,河原能久.丁坝群近体流动结构的可视化实验研究[J].水利学报,2000,3：42-47.
[19]陈志昌,罗小峰.长江口深水航道治理工程物理模型试验研究成果综述[J].水运工程,2006.12：134-140.
[20]Chen F Y, Ikeda S. Horizontal separation flows in shallow open channels with spur dikes [J]. J. Hydrosci.& Hydaul. Eng., JSCE,1997,15(2):15-30.
[21]应强，焦志斌.丁坝水力学[B]. 海洋出版社，北京，2004.
[22]程年生.丁坝有效影响范围与合理布设[J].水运工程,1991,4：28-31.
[23]杨元平.透水丁坝坝后回流区长度研究[J].水运工程,2005,2：18-21.
[24]韩玉芳,陈志昌.丁坝回流长度的变化[J].水利水运工程学报[J],2004,3：33-36.
[25]曹艳敏,张华庆,蒋昌波,等.丁坝冲刷坑及下游回流区流场和紊动特性试验研究[J].水动力学研究与进展(A辑),2008,23(5)：560-570.
[26]Ho J, Yeo H K, Coonrod J, et al. Numerical modeling study for flow pattern changes induced by single groyne [C].32nd Congress of IAHR, Venice, Italy, CD-ROM,2007.
[27]Molinas A, Kheireldin K, Wu B S. Shear stress around vertical wall abutments [J]. Journal of Hydraulic Engineering,1998,124(8):822-830.
[28]Muneta N, Shimizu Y, Hojo K. Experimental study of river flows with spur-dikes [C].48th Proceedings of Hokkaido Branch,1992.353-358.
[29]Rajaratnam N, Nwachukwu B A. Flow near groin-like structures [J]. Journal of Hydraulic Engineering,1983,109(3):463-480.
[30]Chen F Y, Ikeda S. Horizontal separation flows in shallow open channels with spur dikes [J]. Journal of Hydroscience and Hydraulic Engineering, JSCE,1997,15(2):15-30.
[31]Zhang H, Nakagawa H. Inverstigation on morphological consequences of spur dyke with
experimental and numerical methods [C]. Proc.8th Int. Conf. on Hydrosci & Eng., Nagoya.
[32]Osman M A, Salih A M, Ebrahim A A. Flow pattern around groynes [J]. Sudan Engineering Society Journal,2001,47(39):29-36.
[33]高桂景.丁坝水力特性及冲刷机理研究[D].重庆交通大学,2006.
[34]Johnson P A, Dock D A. Probabilistic bridge scour estimate [J]. Journal of Hydraulic Engineering,1998,124(7):750-754.
[35]Yasi M. Uncertainties in the simulation of bed evolution in recirculation flow area behind groynes [J]. Iranian Journal of Science & Technology B, Engineering,30(B1):69-84.
[36]Prohaska S, Jancke T, Westrich B. Model based estimation of sediment erosion in groyne fields along the River Elbe [C]. XXIVth Conference of the Danubian Countries, IOP Conf. Series:Earth and Environmental Science,2008.1-11.
[37]Coleman S E, Lauchlan C S, Melville B W. Clear-water scour development at bridge abutments [J]. J. Hydraul. Res.,2003,41(5):521-531.
[38]Dey S, Barbhuiya A K. Time variation of scour at abutments [J]. Journal of Hydraulic Engineering,2005,131(1):11-24.
[39]Nasrollahi A, Ghodsian M, Neyshabouri S A A S. Local scour at permeable spur dikes [J]. Journal of Applied Sciences,2008,1-9.
[40]Melville B W. Local scour at bridge abutments [J]. J. Hydraul. Eng.,1992,118(4):615-631.
[41]Rahman M M, Haque M A. Local scour at sloped-wall spur-dike-like structures in alluvial rivers [J]. Journal of Hydraulic Engineering,2004,130(1):70-75.
[42]韩玉芳.丁坝的造床作用研究.博士论文,南京水利科学研究院,2003.
[43]应强.淹没丁坝附近的水流流态[J].河海大学学报,1995,23(4)：62-68.
[44]方达宪,王军.漫水丁坝上游面边坡陡度对冲深影响的试验研究[J].华东公路,1989,5：57-59.
[45]张义青,田伟平,赵殿英.漫水丁坝和丁坝群防护的试验研究[J].西安公路交通大学学报,1999,19(4)：63-65.
[46]汪德胜.漫水丁坝局部冲刷的研究[J].水动力学研究与进展(A辑),1988,3(2)：60-69.
[47]Elawady E, Michiue M, Hinokidani O. Experimental study of flow behavior around submerged spur-dike on rigid bed [J]. Annual Journal of Hydraulic Engineering, JSCE,2000, 44:539-544.
[48]B.A.培什金编,谢鉴衡,胡孝渊合译.河道整治,中国工业出版社,1965.92-94.
[49]李国斌.淹没丁坝水流试验研究及三维数值计算.南京水利科学研究院,1989.
[50]Kuhnle R A, Jia Y F, Alonso C V. Measured and Simulated Flow near a Submerged Spur Dike [J]. J. Hydraul. Eng.,2008,134(7):916-924.
[51]Zhang H, Nakagawa H, Muto Yasunori, et al. Bed deformation around groins in a river restoration project [J]. Annual Journal of Hydraulic Engineering, JSCE,2007,51:127-132.
[52]赵连白.淹没丁坝群水力计算的试验研究[J].水科学进展,1994,5(3)：221-228.
[53]汪德胜.漫水丁坝若干水力学问题试验研究[D].研究生论文.合肥：合肥工业大学,1988.
[54]陈国祥,张锦琦,陈耀庭.淹没丁坝壅水规律试验研究[J].河海大学学报,1991,19(5)：88-93.
[55]应强,孔祥柏.淹没丁坝群壅水试验研究[J].水利水运科学研究,1995,1：13～21.
[56]Kuhnle R A, Alonso C V, Jr. F D S. Geometry of scour holes associated with 90° spur dikes [J]. Journal of Hydraulic Engineering,1999,125(9):972-978.
[57]Kuhnle R A, Alonso C V, Jr. F D S. Local scour associated with angled spur dikes [J]. Journal of Hydraulic Engineering,2002,128(12):1087-1093.
[58]程年生,李昌华.丁坝绕流的κ-ε紊流模型数值解[J].水利水运科学研究,1989,3：11-23.
[59]陆永军,徐成伟.用κ-ε紊流模式模拟丁坝绕流[J].水利学报,1991,3：67-73.
[60]Molls T, Chaudhry M H, Khan K W. Numerical simulation of two-dimensional flow near a spur-dike [J]. Advances in Water Resources,1995,18(4):227-236.
[61]李中伟,余明辉,段文忠,等.丁坝附近局部流场的数值模拟[J].武汉水利电力大学学报,2000,33(3)：18-22.
[62]潘军峰,冯民权,郑邦民,等.丁坝绕流及局部冲刷坑二维数值模拟[J].四川大学学报(工程科学版),2005,37(1)：15-18.
[63]Molinas A, Hafez Y I. Finite element surface model for flow around vertical wall abutments [J]. Journal of Fluids and Structures,2000,14:711-733.
[64]黄文典,李嘉,李志勤.淹没丁坝平面二维水流数值模拟研究[J].四川大学学报(工程科学版),2005,37(1)：19-23.
[65]李浩麟,项有法.河口航道二维潮流的单元积分解法[J].水利学报,1984,11：66-72.
[66]夏云峰,孙梅秀,李昌华.用水深平均κ-ε紊流模型计算淹没丁坝流场[J].水利水运科学研究,1993,2：109-118.
[67]李国斌,李昌华.天然河道淹没丁坝群水流计算平面二维流带模型[J].泥沙研究,1994,4：40-49.
[68]李国斌,韩信.天然河道淹没丁坝群水深平均平面二维数学模型研究[J].水动力学研究与进展(A辑),2001,16(2)：230-237.
[69]Tingsanchali T, Maheswaran S.2-D depth-averaged flow computation near groyne [J]. Journal of Hydraulic Engineering,1990,116(1):71-86.
[70]Muneta N, Shimizu Y. Nuemrical analysis model with spur-dikes considering the vertical flow velocity distribution [J]. Journal of Hydraulic, Coastal & Environmetal Engineering, JSCE,1994,497(28):31-39.
[71]彭静,河源能久,玉井信行.线性与非线性紊流模型及其在丁坝绕流中的应用[J].水动力学研究与进展(A辑),2003,18(5)：589-594.
[72]崔占峰,张小峰.三维紊流模型在丁坝中的应用[J].武汉大学学报(工学版),2006,39(1)：15-20.
[73]马福喜,田景环.丁坝群三维水流数值研究[J].应用基础与工程科学学报,1995,3(2)：188-193.
[74]李志勤,李洪,李嘉,等.溢流丁坝附近自由水面的实验研究与数值模拟[J].水利学报,2003.8：53-57.
[75]Ouillon S, Dartus D. Three-dimensional computation of flow around groyne [J]. Journal of Hydraulic Engineering,1997,123(11):962-970.
[76]假冬冬,邵学军,周刚.大系数法与壁函数结合在丁坝绕流三维数值模拟中的应用[J].水利水运工程学报,2008,1：72-77.
[77]Nagata N, Hosoda T, Nakato T, et al. Three-dimensional numerical model for flow and bed deformation around river hydraulic structures [J]. Journal of Hydraulic Engineering,2005, 131(12):1074-1088.
[78]Akahori R, Schmeeckle M. Numerical analysis of secondary-flow around a spur dike using a three-dimensional free water surface LES model [C]. River, Coastal and Estuarine Morphodynamics:RCEM 2005.921-930.
[79]Mayerle R, Toro F M, Wang S S Y. Verification of a three-dimensional numerical model simulation of the flow in the vicinity of spur dikes [J]. J. Hydraul. Res.,1995,33(2), 243-255.
[80]陆永军,赵连白,袁美琦.航槽三维流动的数学模型[J].水道港口,1995,4：24-31.
[81]胡德超,张红武,钟德钰.C-D无结构网格上的三维自由水面非静水压力流动模型Ⅰ：算法[J].水利学报,2009,40(8)：948-955.
[82]胡德超,张红武,钟德钰.C-D无结构网格上的三维自由水面非静水压力流动模型Ⅱ：验证[J].水利学报,2009,40(9)：1077-1084.
[83]吕彪,金生,艾丛芳.基于非结构化网格上的三维微幅自由表面流动非静压数值模型[J].水动力学研究与进展(A辑),2009,24(3)：350-357.
[84]Zhang H, Nakagawa H, Ishigaki T, et al. A RANS solver using a 3D unstructured FVM Procedure [J]. Annuals of Disas. Prev. Res. Inst.,2005,48B:691-707.
[85]林秀维,陈阳.Prandtl混合长紊流模型模拟丁坝绕流[J].水道港口,1998,2：47-49.
[86]周宜林.淹没丁坝附近三维水流运动大涡数值模拟[J].长江科学院院报,2001,18(5)：28-32.
[87]Spalding B D, Svensson U. The development and erosion of the thermocline [B]. Heat transfer and turbulent buoyant convection, studies and applications, for natural environment, buildings, engineering systems, D B Spalding and N Afgon, eds., Hemisphere, Washionton, D.C.
[88]Ye J, Dou G R. A new turbulence model:The K-\Gj-S model [C]. Proc., Int. Symp. on Sediment Transport Modeling, ASCE,1989, New Orleans,184-189.
[89]叶坚,窦国仁.一种新的紊流模型K-e-S模型[J].水利水运科学研究,1990,3：1-10.
[90]Lu Y J, Wang Z Y.3D numerical simulation for water flows and sediment deposition in dam areas of the Three Gorges Project [J]. Journal of Hydraulic Engineering,2009,135(9): 755-769.
[91]Mellor G L, Blumberg A F. Modeling vertical and horizontal diffusivities with the sigma coordinate system [J]. Monthly Weather Review,1985,113(8):1379-1383.
[92]Huang W, Spaulding M. Modeling horizontal diffusion with sigma coordinate system [J]. Journal of Hydraulic Engineering,1996,122(6):349-352.
[93]Haney R L. On the pressure gradient force over steep topography in sigma coordinate ocean models [J]. Journal of Physics Oceanography,1991,21:610-619.
[94]Huang W, Spaulding M. Reducing horizontal diffusion errors in a-coordinate coastal ocean models with a second-order Lagrangian-interpolation finite-difference scheme [J]. Ocean Engineering,2002,29(5):495-512.
[95]张景新,刘桦.σ坐标系下水平扩散项的有限差分计算[J].力学季刊,2006,27(3)：377-386.
[96]谭维炎,胡四一.计算浅水动力学的新方向[J].水科学进展,1992,3(4)：310-318.
[97]Alcrudo F, Garcia-Navarro P. A high-resolution Godunov-type scheme in finite volumes for the 2D Shallow-Water Equations [J]. International Journal for Numerical Methods in Fluids, 1993,16:489-505.
[98]Mingham C G, Causon D M. High-resolution finite-volume method for shallow water flows [J]. Journal of Hydraulic Engineering,1998,124(6):605-614.
[99]胡四一,施勇,王银堂,等.长江中下游河湖洪水演进的数值模拟[J].水科学进展,2002,13(3)：278-286.
[100]谭维炎,胡四一,韩曾萃,等.钱塘江口涌潮的二维数值模拟[J].水科学进展,1995,6(2)：83-93.
[101]李未,张长宽,王如云.基于无结构网格有限体积法的风暴潮数值预报模式[J].热带海洋学报,2007,26(2)：9-14.
[102]刘臻,史宏达,黄燕.一种基于Roe格式的有限体积法在二维溃坝问题中的应用[J].中国海洋大学学报,2007,37(2)：323-327.
[103]张大伟,张超,王兴奎.具有实际地形的溃堤水流数值模拟[J].清华大学学报(自然科学版),2007,47(12)：2127-2130.
[104]王志力,耿艳芬,金生.二维洪水演进数值模拟[J].计算力学学报,2007,24(4)：533-538.
[105]褚克坚,华祖林,王惠民.二维浅水水流的一种新型三角形网格FVM计算格式[J].河海大学学报(自然科学版),2003,31(4)：370-373.
[106]孔俊,宋志尧,张红贵.非结构型浅水方程数值模式的建立及应用[J].河海大学学报(自然科学版),2006,34(4)：456-459.
[107]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[J].水科学进展,2000,11(4)：368-374.
[108]施勇,胡四一.无结构网格上平面二维水沙模拟的有限体积法[J].水科学进展,2002,13(4)：409-415.
[109]李绍武,卢丽锋,时钟.河口准三维涌潮数学模型研究[J].水动力学研究与进展(A辑),2004,19(4)：407-415.
[110]赖锡军,曲卓杰,周杰,等.非结构网格上的三维浅水流动数值模型[J].水科学进展,2006,17(5)：693-699.
[111]胡四一,谭维炎.无结构网格上二维浅水流动的数值模拟[J].水科学进展,1995,6(1)：1-9.
[112]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)：262-270.
[113]LeVeque R J. Balancing source terms and flux gradients in high-resolution Godunov methods:the quasi-steady wave-propagation algorithm [J]. Journal of Computational Physics,1998,146:346-365.
[114]Hubbard M E, Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients [J]. Journal of Computational Physics,2000,165:89-125.
[115]Zhou J G, Causon D M, Mingham C G, et al. The Surface Gradient Method for the treatment of source terms in the Shallow-Water Equations [J]. Journal of Computational Physics,2001, 168:1-25.
[116]Rogers B D, Borthwick A G L, Taylor P H. Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver [J]. Journal of Computational Physics,2003,192:422-451.
[117]潘存鸿.三角形网格下求解二维浅水方程的和谐Godunov格式[J].水科学进展,2007,18(2)：204-209.
[118]Komaei S. An improved, robust implicit solution for the two-dimensional shallow water equations on unstructured grids [C]. Proc.2nd Int. Conf. on Fluvial Hydraulics, M. Greco, ed.,2004.1065-1072.
[119]艾丛芳，金生.基于三角形网絡求解二维浅水方程的改进的HLL方法[J]. 水动力学研究与进展(A辑),2007,22(6)：723-729.
[120]于守兵.计算二维浅水方程中静水压力项与底坡项的积分平衡法[J].水利水电科技进展,2009,29(4)：32-35.
[121]Holtz K P. Numerical simulation of recirculating flow at groynes [C]. Computer methonds in water resources, Brebbia C A, Ouazar D, Sari D B, eds., Vol.2, NO.2, Springer Verlag, New York, Inc., New York, N. Y,1991,463-477.
[122]Engelund F. Flow and bed topography in channel bends [J]. Journal of the Hydraulics Division,1974,100:1631-1648.
[123]Zhu J, Shih T H. Calculations of turbulent separated flows with two-equation turbulence models [J]. Computational Fluid Dynamics,1994,3:343-354.
[124]Kawahara Y, Peng J. Three-dimensional numerical simulation of flood flows around groins [C]. Proc.2nd Asian Computational Fluid Dynamics Conference,1996.539-544.
[125]Shih T H, Zhu J, Lumley J L. A new Reynolds stress algebraic equation model [J]. Comput. Methods Appl. Mech. Eng.,1995,125:287-302.
[126]McCoy A, Constantinescu G, Weber L J. Numerical investigation of flow hydrodynamics in a channel with a series of groynes [J]. Journal of Hydraulic Engineering,2008,134(2): 157-173.
[127]宋志尧,薛鸿超,严以新.线边界法在潮流模拟中的应用[J].海洋工程,2000,18(4)：49-54.
[128]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[J].水动力学研究与进展(A辑),2006,21(1)：102-106.
[129]Akanbi A A, Katopodes N D. Model for flood propogation on initially dry land [J]. Journal of Hydraulic Engineering,1987,114(15):689-706.
[130]毛献忠,潘存鸿.移动边界浅水问题的数值研究[J].水动力学研究与进展(A辑),2002,17(4)：507-513.
[131]何少苓,陆吉康.三维动边界破开算子法不恒定流模拟研究[J].水利学报,1998,8：8-13.
[132]孙英兰,张越美.胶州湾三维变动边界的潮流数值模拟[J].海洋与湖沼,2001,32(4)：355-362.
[133]Tominaga A, Chiba S. Flow structure around a submerged spur dike [C]. Proc. of Annual Meeting of Japan Society of Fluid Mechanics,1996.317-318.
[134]Han Y F, Chen Z C. Experimental study on local scour around bridge piers in tidal current [J]. China Ocean Engineering,2004,18(4):669-676.
[135]朱伯荣,陈志昌,罗小峰.长江口河工模型试验中的仪器设备[J].水利水运工程学报,2005,1：63-66.
[136]赵晓冬,吴丽华,陈志昌等.河口整治工程建筑物局部冲刷试验研究[J].海洋工程,2005,23(1)：47～52.
[2]马颖,江恩惠,李军华,等.丁坝在莱茵河整治中的作用[J].人民长江,2008,39(5)：77-79.
[3]陈志昌,乐嘉钻.长江口深水航道整治原理[J].水利水运工程学报,2005,1：1-7.
[4]窦国仁.窦国仁论文集[C].北京：中国水利水电出版社,2003.260-279.
[5]程年生,李昌华.有边坡丁坝回流试验研究[J].水利水运科学研究,1991,2：123-132.
[6]冯永忠.错口丁坝回流尺度的研究[J].河海大学学报,1995,23(4)：69-76.
[7]乐培九,李旺生,杨细根.丁坝回流长度[J].水道港口,1999,2：3-9.
[8]李国斌,韩信,傅津先.非淹没丁坝下游回流长度及最大回流宽度研究[J].泥沙研究,2001,3：68-73.
[9]孔祥柏,胡美英,吴济难,等.丁坝对水流影响的试验研究[J].水利水运科学研究,1983,68-78.
[10]Lu Y J, Zhou Y T. Flow mechanism and velocity field near groin-like structures [J]. Journal of China Ocean Engineering,1989,3(2):203-216.
[11]应强,孔祥柏.非等长淹没丁坝群局部水头损失的计算[J].水科学进展,1994,5(3)：214-220.
[12]孔祥柏,程年生.丁、潜坝局部水头损失的试验研究[J].水利水运科学研究,1992,4：387-395.
[13]Azinfar H, Kells J A. Backwater effect due to a single spur dike [J]. Can. J. Civ. Eng.,2007, 34:107-115.
[14]Muto Y, Baba Y, Aya S. Velocity measurements in open channel flow with rectangular embayments formed by spur dikes [J]. Annuals of Disas. Prev. Inst.,2002,45(B2):449-457.
[15]Wu B S, Wang G Q, Ma J M, et al. Case study:river training and its effects on fluvial processes in the Lower Yellow River, China [J]. Journal of Hydraulic Engineering,2005, 131(2):85-97.
[16]Anlanger C, Sukhodolov A, Schnauder I, et al. Impact of submerged groynes on the flow field results from a field experiment at the river Spree, Germany [C]. EGU General Assembly,2008, Vienna, Austria. EGU2008-A-11145.
[17]陈稚聪,黑鹏飞,丁翔.丁坝回流区水流紊动强度试验[J].清华大学学报(自然科学版),2008,48(12)：2053-2056.
[18]彭静,河原能久.丁坝群近体流动结构的可视化实验研究[J].水利学报,2000,3：42-47.
[19]陈志昌,罗小峰.长江口深水航道治理工程物理模型试验研究成果综述[J].水运工程,2006.12：134-140.
[20]Chen F Y, Ikeda S. Horizontal separation flows in shallow open channels with spur dikes [J]. J. Hydrosci.& Hydaul. Eng., JSCE,1997,15(2):15-30.
[21]应强，焦志斌.丁坝水力学[B]. 海洋出版社，北京，2004.
[22]程年生.丁坝有效影响范围与合理布设[J].水运工程,1991,4：28-31.
[23]杨元平.透水丁坝坝后回流区长度研究[J].水运工程,2005,2：18-21.
[24]韩玉芳,陈志昌.丁坝回流长度的变化[J].水利水运工程学报[J],2004,3：33-36.
[25]曹艳敏,张华庆,蒋昌波,等.丁坝冲刷坑及下游回流区流场和紊动特性试验研究[J].水动力学研究与进展(A辑),2008,23(5)：560-570.
[26]Ho J, Yeo H K, Coonrod J, et al. Numerical modeling study for flow pattern changes induced by single groyne [C].32nd Congress of IAHR, Venice, Italy, CD-ROM,2007.
[27]Molinas A, Kheireldin K, Wu B S. Shear stress around vertical wall abutments [J]. Journal of Hydraulic Engineering,1998,124(8):822-830.
[28]Muneta N, Shimizu Y, Hojo K. Experimental study of river flows with spur-dikes [C].48th Proceedings of Hokkaido Branch,1992.353-358.
[29]Rajaratnam N, Nwachukwu B A. Flow near groin-like structures [J]. Journal of Hydraulic Engineering,1983,109(3):463-480.
[30]Chen F Y, Ikeda S. Horizontal separation flows in shallow open channels with spur dikes [J]. Journal of Hydroscience and Hydraulic Engineering, JSCE,1997,15(2):15-30.
[31]Zhang H, Nakagawa H. Inverstigation on morphological consequences of spur dyke with
experimental and numerical methods [C]. Proc.8th Int. Conf. on Hydrosci & Eng., Nagoya.
[32]Osman M A, Salih A M, Ebrahim A A. Flow pattern around groynes [J]. Sudan Engineering Society Journal,2001,47(39):29-36.
[33]高桂景.丁坝水力特性及冲刷机理研究[D].重庆交通大学,2006.
[34]Johnson P A, Dock D A. Probabilistic bridge scour estimate [J]. Journal of Hydraulic Engineering,1998,124(7):750-754.
[35]Yasi M. Uncertainties in the simulation of bed evolution in recirculation flow area behind groynes [J]. Iranian Journal of Science & Technology B, Engineering,30(B1):69-84.
[36]Prohaska S, Jancke T, Westrich B. Model based estimation of sediment erosion in groyne fields along the River Elbe [C]. XXIVth Conference of the Danubian Countries, IOP Conf. Series:Earth and Environmental Science,2008.1-11.
[37]Coleman S E, Lauchlan C S, Melville B W. Clear-water scour development at bridge abutments [J]. J. Hydraul. Res.,2003,41(5):521-531.
[38]Dey S, Barbhuiya A K. Time variation of scour at abutments [J]. Journal of Hydraulic Engineering,2005,131(1):11-24.
[39]Nasrollahi A, Ghodsian M, Neyshabouri S A A S. Local scour at permeable spur dikes [J]. Journal of Applied Sciences,2008,1-9.
[40]Melville B W. Local scour at bridge abutments [J]. J. Hydraul. Eng.,1992,118(4):615-631.
[41]Rahman M M, Haque M A. Local scour at sloped-wall spur-dike-like structures in alluvial rivers [J]. Journal of Hydraulic Engineering,2004,130(1):70-75.
[42]韩玉芳.丁坝的造床作用研究.博士论文,南京水利科学研究院,2003.
[43]应强.淹没丁坝附近的水流流态[J].河海大学学报,1995,23(4)：62-68.
[44]方达宪,王军.漫水丁坝上游面边坡陡度对冲深影响的试验研究[J].华东公路,1989,5：57-59.
[45]张义青,田伟平,赵殿英.漫水丁坝和丁坝群防护的试验研究[J].西安公路交通大学学报,1999,19(4)：63-65.
[46]汪德胜.漫水丁坝局部冲刷的研究[J].水动力学研究与进展(A辑),1988,3(2)：60-69.
[47]Elawady E, Michiue M, Hinokidani O. Experimental study of flow behavior around submerged spur-dike on rigid bed [J]. Annual Journal of Hydraulic Engineering, JSCE,2000, 44:539-544.
[48]B.A.培什金编,谢鉴衡,胡孝渊合译.河道整治,中国工业出版社,1965.92-94.
[49]李国斌.淹没丁坝水流试验研究及三维数值计算.南京水利科学研究院,1989.
[50]Kuhnle R A, Jia Y F, Alonso C V. Measured and Simulated Flow near a Submerged Spur Dike [J]. J. Hydraul. Eng.,2008,134(7):916-924.
[51]Zhang H, Nakagawa H, Muto Yasunori, et al. Bed deformation around groins in a river restoration project [J]. Annual Journal of Hydraulic Engineering, JSCE,2007,51:127-132.
[52]赵连白.淹没丁坝群水力计算的试验研究[J].水科学进展,1994,5(3)：221-228.
[53]汪德胜.漫水丁坝若干水力学问题试验研究[D].研究生论文.合肥：合肥工业大学,1988.
[54]陈国祥,张锦琦,陈耀庭.淹没丁坝壅水规律试验研究[J].河海大学学报,1991,19(5)：88-93.
[55]应强,孔祥柏.淹没丁坝群壅水试验研究[J].水利水运科学研究,1995,1：13～21.
[56]Kuhnle R A, Alonso C V, Jr. F D S. Geometry of scour holes associated with 90° spur dikes [J]. Journal of Hydraulic Engineering,1999,125(9):972-978.
[57]Kuhnle R A, Alonso C V, Jr. F D S. Local scour associated with angled spur dikes [J]. Journal of Hydraulic Engineering,2002,128(12):1087-1093.
[58]程年生,李昌华.丁坝绕流的κ-ε紊流模型数值解[J].水利水运科学研究,1989,3：11-23.
[59]陆永军,徐成伟.用κ-ε紊流模式模拟丁坝绕流[J].水利学报,1991,3：67-73.
[60]Molls T, Chaudhry M H, Khan K W. Numerical simulation of two-dimensional flow near a spur-dike [J]. Advances in Water Resources,1995,18(4):227-236.
[61]李中伟,余明辉,段文忠,等.丁坝附近局部流场的数值模拟[J].武汉水利电力大学学报,2000,33(3)：18-22.
[62]潘军峰,冯民权,郑邦民,等.丁坝绕流及局部冲刷坑二维数值模拟[J].四川大学学报(工程科学版),2005,37(1)：15-18.
[63]Molinas A, Hafez Y I. Finite element surface model for flow around vertical wall abutments [J]. Journal of Fluids and Structures,2000,14:711-733.
[64]黄文典,李嘉,李志勤.淹没丁坝平面二维水流数值模拟研究[J].四川大学学报(工程科学版),2005,37(1)：19-23.
[65]李浩麟,项有法.河口航道二维潮流的单元积分解法[J].水利学报,1984,11：66-72.
[66]夏云峰,孙梅秀,李昌华.用水深平均κ-ε紊流模型计算淹没丁坝流场[J].水利水运科学研究,1993,2：109-118.
[67]李国斌,李昌华.天然河道淹没丁坝群水流计算平面二维流带模型[J].泥沙研究,1994,4：40-49.
[68]李国斌,韩信.天然河道淹没丁坝群水深平均平面二维数学模型研究[J].水动力学研究与进展(A辑),2001,16(2)：230-237.
[69]Tingsanchali T, Maheswaran S.2-D depth-averaged flow computation near groyne [J]. Journal of Hydraulic Engineering,1990,116(1):71-86.
[70]Muneta N, Shimizu Y. Nuemrical analysis model with spur-dikes considering the vertical flow velocity distribution [J]. Journal of Hydraulic, Coastal & Environmetal Engineering, JSCE,1994,497(28):31-39.
[71]彭静,河源能久,玉井信行.线性与非线性紊流模型及其在丁坝绕流中的应用[J].水动力学研究与进展(A辑),2003,18(5)：589-594.
[72]崔占峰,张小峰.三维紊流模型在丁坝中的应用[J].武汉大学学报(工学版),2006,39(1)：15-20.
[73]马福喜,田景环.丁坝群三维水流数值研究[J].应用基础与工程科学学报,1995,3(2)：188-193.
[74]李志勤,李洪,李嘉,等.溢流丁坝附近自由水面的实验研究与数值模拟[J].水利学报,2003.8：53-57.
[75]Ouillon S, Dartus D. Three-dimensional computation of flow around groyne [J]. Journal of Hydraulic Engineering,1997,123(11):962-970.
[76]假冬冬,邵学军,周刚.大系数法与壁函数结合在丁坝绕流三维数值模拟中的应用[J].水利水运工程学报,2008,1：72-77.
[77]Nagata N, Hosoda T, Nakato T, et al. Three-dimensional numerical model for flow and bed deformation around river hydraulic structures [J]. Journal of Hydraulic Engineering,2005, 131(12):1074-1088.
[78]Akahori R, Schmeeckle M. Numerical analysis of secondary-flow around a spur dike using a three-dimensional free water surface LES model [C]. River, Coastal and Estuarine Morphodynamics:RCEM 2005.921-930.
[79]Mayerle R, Toro F M, Wang S S Y. Verification of a three-dimensional numerical model simulation of the flow in the vicinity of spur dikes [J]. J. Hydraul. Res.,1995,33(2), 243-255.
[80]陆永军,赵连白,袁美琦.航槽三维流动的数学模型[J].水道港口,1995,4：24-31.
[81]胡德超,张红武,钟德钰.C-D无结构网格上的三维自由水面非静水压力流动模型Ⅰ：算法[J].水利学报,2009,40(8)：948-955.
[82]胡德超,张红武,钟德钰.C-D无结构网格上的三维自由水面非静水压力流动模型Ⅱ：验证[J].水利学报,2009,40(9)：1077-1084.
[83]吕彪,金生,艾丛芳.基于非结构化网格上的三维微幅自由表面流动非静压数值模型[J].水动力学研究与进展(A辑),2009,24(3)：350-357.
[84]Zhang H, Nakagawa H, Ishigaki T, et al. A RANS solver using a 3D unstructured FVM Procedure [J]. Annuals of Disas. Prev. Res. Inst.,2005,48B:691-707.
[85]林秀维,陈阳.Prandtl混合长紊流模型模拟丁坝绕流[J].水道港口,1998,2：47-49.
[86]周宜林.淹没丁坝附近三维水流运动大涡数值模拟[J].长江科学院院报,2001,18(5)：28-32.
[87]Spalding B D, Svensson U. The development and erosion of the thermocline [B]. Heat transfer and turbulent buoyant convection, studies and applications, for natural environment, buildings, engineering systems, D B Spalding and N Afgon, eds., Hemisphere, Washionton, D.C.
[88]Ye J, Dou G R. A new turbulence model:The K-\Gj-S model [C]. Proc., Int. Symp. on Sediment Transport Modeling, ASCE,1989, New Orleans,184-189.
[89]叶坚,窦国仁.一种新的紊流模型K-e-S模型[J].水利水运科学研究,1990,3：1-10.
[90]Lu Y J, Wang Z Y.3D numerical simulation for water flows and sediment deposition in dam areas of the Three Gorges Project [J]. Journal of Hydraulic Engineering,2009,135(9): 755-769.
[91]Mellor G L, Blumberg A F. Modeling vertical and horizontal diffusivities with the sigma coordinate system [J]. Monthly Weather Review,1985,113(8):1379-1383.
[92]Huang W, Spaulding M. Modeling horizontal diffusion with sigma coordinate system [J]. Journal of Hydraulic Engineering,1996,122(6):349-352.
[93]Haney R L. On the pressure gradient force over steep topography in sigma coordinate ocean models [J]. Journal of Physics Oceanography,1991,21:610-619.
[94]Huang W, Spaulding M. Reducing horizontal diffusion errors in a-coordinate coastal ocean models with a second-order Lagrangian-interpolation finite-difference scheme [J]. Ocean Engineering,2002,29(5):495-512.
[95]张景新,刘桦.σ坐标系下水平扩散项的有限差分计算[J].力学季刊,2006,27(3)：377-386.
[96]谭维炎,胡四一.计算浅水动力学的新方向[J].水科学进展,1992,3(4)：310-318.
[97]Alcrudo F, Garcia-Navarro P. A high-resolution Godunov-type scheme in finite volumes for the 2D Shallow-Water Equations [J]. International Journal for Numerical Methods in Fluids, 1993,16:489-505.
[98]Mingham C G, Causon D M. High-resolution finite-volume method for shallow water flows [J]. Journal of Hydraulic Engineering,1998,124(6):605-614.
[99]胡四一,施勇,王银堂,等.长江中下游河湖洪水演进的数值模拟[J].水科学进展,2002,13(3)：278-286.
[100]谭维炎,胡四一,韩曾萃,等.钱塘江口涌潮的二维数值模拟[J].水科学进展,1995,6(2)：83-93.
[101]李未,张长宽,王如云.基于无结构网格有限体积法的风暴潮数值预报模式[J].热带海洋学报,2007,26(2)：9-14.
[102]刘臻,史宏达,黄燕.一种基于Roe格式的有限体积法在二维溃坝问题中的应用[J].中国海洋大学学报,2007,37(2)：323-327.
[103]张大伟,张超,王兴奎.具有实际地形的溃堤水流数值模拟[J].清华大学学报(自然科学版),2007,47(12)：2127-2130.
[104]王志力,耿艳芬,金生.二维洪水演进数值模拟[J].计算力学学报,2007,24(4)：533-538.
[105]褚克坚,华祖林,王惠民.二维浅水水流的一种新型三角形网格FVM计算格式[J].河海大学学报(自然科学版),2003,31(4)：370-373.
[106]孔俊,宋志尧,张红贵.非结构型浅水方程数值模式的建立及应用[J].河海大学学报(自然科学版),2006,34(4)：456-459.
[107]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[J].水科学进展,2000,11(4)：368-374.
[108]施勇,胡四一.无结构网格上平面二维水沙模拟的有限体积法[J].水科学进展,2002,13(4)：409-415.
[109]李绍武,卢丽锋,时钟.河口准三维涌潮数学模型研究[J].水动力学研究与进展(A辑),2004,19(4)：407-415.
[110]赖锡军,曲卓杰,周杰,等.非结构网格上的三维浅水流动数值模型[J].水科学进展,2006,17(5)：693-699.
[111]胡四一,谭维炎.无结构网格上二维浅水流动的数值模拟[J].水科学进展,1995,6(1)：1-9.
[112]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)：262-270.
[113]LeVeque R J. Balancing source terms and flux gradients in high-resolution Godunov methods:the quasi-steady wave-propagation algorithm [J]. Journal of Computational Physics,1998,146:346-365.
[114]Hubbard M E, Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients [J]. Journal of Computational Physics,2000,165:89-125.
[115]Zhou J G, Causon D M, Mingham C G, et al. The Surface Gradient Method for the treatment of source terms in the Shallow-Water Equations [J]. Journal of Computational Physics,2001, 168:1-25.
[116]Rogers B D, Borthwick A G L, Taylor P H. Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver [J]. Journal of Computational Physics,2003,192:422-451.
[117]潘存鸿.三角形网格下求解二维浅水方程的和谐Godunov格式[J].水科学进展,2007,18(2)：204-209.
[118]Komaei S. An improved, robust implicit solution for the two-dimensional shallow water equations on unstructured grids [C]. Proc.2nd Int. Conf. on Fluvial Hydraulics, M. Greco, ed.,2004.1065-1072.
[119]艾丛芳，金生.基于三角形网絡求解二维浅水方程的改进的HLL方法[J]. 水动力学研究与进展(A辑),2007,22(6)：723-729.
[120]于守兵.计算二维浅水方程中静水压力项与底坡项的积分平衡法[J].水利水电科技进展,2009,29(4)：32-35.
[121]Holtz K P. Numerical simulation of recirculating flow at groynes [C]. Computer methonds in water resources, Brebbia C A, Ouazar D, Sari D B, eds., Vol.2, NO.2, Springer Verlag, New York, Inc., New York, N. Y,1991,463-477.
[122]Engelund F. Flow and bed topography in channel bends [J]. Journal of the Hydraulics Division,1974,100:1631-1648.
[123]Zhu J, Shih T H. Calculations of turbulent separated flows with two-equation turbulence models [J]. Computational Fluid Dynamics,1994,3:343-354.
[124]Kawahara Y, Peng J. Three-dimensional numerical simulation of flood flows around groins [C]. Proc.2nd Asian Computational Fluid Dynamics Conference,1996.539-544.
[125]Shih T H, Zhu J, Lumley J L. A new Reynolds stress algebraic equation model [J]. Comput. Methods Appl. Mech. Eng.,1995,125:287-302.
[126]McCoy A, Constantinescu G, Weber L J. Numerical investigation of flow hydrodynamics in a channel with a series of groynes [J]. Journal of Hydraulic Engineering,2008,134(2): 157-173.
[127]宋志尧,薛鸿超,严以新.线边界法在潮流模拟中的应用[J].海洋工程,2000,18(4)：49-54.
[128]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[J].水动力学研究与进展(A辑),2006,21(1)：102-106.
[129]Akanbi A A, Katopodes N D. Model for flood propogation on initially dry land [J]. Journal of Hydraulic Engineering,1987,114(15):689-706.
[130]毛献忠,潘存鸿.移动边界浅水问题的数值研究[J].水动力学研究与进展(A辑),2002,17(4)：507-513.
[131]何少苓,陆吉康.三维动边界破开算子法不恒定流模拟研究[J].水利学报,1998,8：8-13.
[132]孙英兰,张越美.胶州湾三维变动边界的潮流数值模拟[J].海洋与湖沼,2001,32(4)：355-362.
[133]Tominaga A, Chiba S. Flow structure around a submerged spur dike [C]. Proc. of Annual Meeting of Japan Society of Fluid Mechanics,1996.317-318.
[134]Han Y F, Chen Z C. Experimental study on local scour around bridge piers in tidal current [J]. China Ocean Engineering,2004,18(4):669-676.
[135]朱伯荣,陈志昌,罗小峰.长江口河工模型试验中的仪器设备[J].水利水运工程学报,2005,1：63-66.
[136]赵晓冬,吴丽华,陈志昌等.河口整治工程建筑物局部冲刷试验研究[J].海洋工程,2005,23(1)：47～52.