近岸波浪对结构物作用耦合数值模型及其工程应用
摘要
Boussinesq方程作为三维势流模型的平面二维近似，能够解决非线性波
浪在较大浅水区域（如港口和一定的海岸区域）上的传播变形问题；另一方
面，作为深度平均模型，Boussinesq方程难以给出结构物附近流动随深度变
化的特征，无法解决波浪对潜堤、浮体等结构物作用问题。而数值求解三维
势流模型或粘流模型的计算量和占用计算机的存储空间都很大，一般只在较
小的计算区域上（如结构物附近）求解，难以直接用于大区域上（考虑波浪
变形）的波浪-结构相互作用问题。另外，势流模型本身决定了结构物附近粘
性流动的特点（如涡度、边界层等）都被忽略了，而要得到流动的这些信息，只
有依靠粘流模型。为能同步和高效率地获得近岸大区域非线性波浪变形特
征、结构物附近三维水动力特征和波浪荷载，结合Boussinesq方程数值模型
和求解N-S方程的VOF方法各自的特点，开展了建立Boussinesq方程和N-
S方程耦合数值模型的研究。
整个研究工作包括以下几部分：
1）建立了有限差分全隐格式Boussinesq方程波浪数值模型。
全隐格式数值模型允许较小的网格尺度，计算过程稳定和结果收敛，并
能保证计算精度以及为与三维模型耦合求解时便于取得相匹配的网格尺
度。在开边界处理上，采取Sommerfeld辐射条件与海绵层吸收结合的
办法，较好地将到达开边界的波浪能量吸收掉。用所建立的Boussinesq
方程波浪数值模型进行了规则波在圆形浅滩上传播变形的数值计算，其
数值结果较好地接近于有关的实验结果，表明所开发的全隐格式
Boussinesq方程波浪数值模型是可靠的，以及具有较高的计算效率，可
以用于近岸大区域波浪变形的数值计算。
2）建立了基于N-S方程和VOF方法的三维数值波浪水池模型。
提出了用于VOF方法的分段式造波机边界条件，并对其它边界相应地给
出了合适的边界条件，建立了基于VOF方法的三维数值波浪水池。数值
试验表明，所提出的分段式造波机边界条件能够产生长时间稳定的波动
过程和斜入射波浪；对开边界的处理上采取了Sommerfeld辐射条件与
海绵层内衰减垂向速度相结合的处理方法，较好地使到达开边界的波浪
透过。数值试验表明所建立的数值波浪水池具有较好的波浪特性，并能
获得较为可靠的结构物波浪荷载结果。
论 丈 摘 要
一
3）建立了 ID Bousj NS－VOF＃合数值模型。
提出了重叠带上压力、速度和波面的匹配边界条件，建立了用二维川S方
程控制内域（包含结构物的近场）流体流动和一维Boussinesq方程控制
外域（内域的外围边界和整个计算域边界所围的区域）流体流动的耦合
数值模型（简称 ID／ZD耦合模型），在时间步进格式下，实现了内域模
型和外域模型同步耦合求解。数模试验显示本文提出的匹配边界条件能
够保证流动在这两个子区域之间光滑而连续地过渡，并且耦合模型模拟
结果（压力、速度、波面和波浪荷载）较好地接近于与原二维NS．VOF
模型的结果。
4）建立了二D BoussinesqoDNS－VOF耦合数值模型。
建立了用三维NS方程控制内域流体流动和二维Boussinesq方程控制
外域流体流动的部分三维化耦合数值模型（简称ZD／3D耦合模型）。数
模试验显示本文提出的压力、速度和波面匹配边界条件在斜人射波浪条
件下是有效性，能够保证流动在两个于区域之间光滑而连续地过渡；还
对耦合模型模拟波面和波浪荷载结果进行了验证，和对耦合模型的计算
效率进行了评估。
5）开展了耦合数值模型在工程数值计算上的觑。
·应用所建立的 ID／ZD耦合模型，进行了消减直立堤前反射波的幕墙
式消浪室性能的数模研究，得到了有意义的研究成果；
·应用所建立的 ZD／3D串联耦合模型对防彼堤堤头附近三维水动力特
征进行了初步研究，得到了有意义的研究成果；
·应用所建立的ZD／3D嵌套耦合模型对港内直立式码头前船舶波浪力
和船体附近三维水动力特征进行了初步研究，得到了有意义的研究
成果。
Abstract
As the depth-averaged simplification of the three-dimensional potential flow
model, the horizontal two-dimensional Boussinesq equations are suitable for
solving efficiently nonlinear wave propagation and transformation in large
shallow water regions (for example, harbor or coastal region with similar size).
On the other hand, because of depth-averaged simplification, the Boussinesq
equations can not be applied in solving such problems as wave actions on
submerged breakwaters, floating bodies etc., in which flow variations with depth
must be considered. For these problems, one must solve potential flow models or
viscous flow models, which are usually applied to a relatively small
computational region around the structure and not suitable for large fluid
domains, this is because both the 3D potential model and the 3D viscous model
are far more CPU time-consuming. Besides, all the flow features attached to
viscosity (vorticity, boundary layer) are disregarded in the modelling by potential
flow theory. One must solve viscous flow models to access these details of flow.
In order to obtain simultaneously and efficiently nonlinear wave
transformations in a harbor or coastal region, details of three dimensional flow
around structures and hydrodynamic loads of wave on marine structures,
combining advantages of Boussinesq model and NS-VOF model, we unfolded the
study of establishing Boussinesq / NS coupled numerical models.
The entire research work includes the following parts:
1) The Boussinesq equations numerical model with implicit differential
method is setup.
Numerical experiments reveal that the implicit method is accurate and
unconditional stable. The Sommerfeld radiation condition (SRC)
combined with sponge layer technique is applied at open boundaries, and
numerical tests verify the performance of SRC assisted by the sponge
layer technique. Computational results of regular waves propagating on a
circular shoal are in good agreement with the experimental data, showing
that the Boussinesq equation numerical model with implicit differential
method can give a satisfactory description of wave transformation over
the topography and can be applied in practical engineering.
2) The three dimensional numerical wave basin (NWB)based on 3D Navier-
Stokes equations and the VOF method is setup.
The wave maker boundary condition for the VOF method is proposed.
On other boundaries, in addition to reflection boundary conditions, the
open boundaries are treated by the technique of velocity reduction
zone(VRZ) at first, in which vertical velocity is reduced exponentially
inside the VRZ. Then Sommerfeld radiation condition is applied at the
open boundary. The performance of the present open boundary treatment
is verified by numerical experiments.
3) The 1D Boussinesq/2D NS-VOF coupled model is set up.
Matching boundary conditions for pressure, velocity and wave surface
elevation on the common matching boundary are proposed, and the
I D/2D coupled numerical model is setup, which is combination of the
2D NS-VOF model applied in the inner region (that is, the near-field
surrounding a marine structure), and the ID Boussinesq model applied in
the outer region. Numerical experiment shows that the present matching
boundary cond
浪在较大浅水区域（如港口和一定的海岸区域）上的传播变形问题；另一方
面，作为深度平均模型，Boussinesq方程难以给出结构物附近流动随深度变
化的特征，无法解决波浪对潜堤、浮体等结构物作用问题。而数值求解三维
势流模型或粘流模型的计算量和占用计算机的存储空间都很大，一般只在较
小的计算区域上（如结构物附近）求解，难以直接用于大区域上（考虑波浪
变形）的波浪-结构相互作用问题。另外，势流模型本身决定了结构物附近粘
性流动的特点（如涡度、边界层等）都被忽略了，而要得到流动的这些信息，只
有依靠粘流模型。为能同步和高效率地获得近岸大区域非线性波浪变形特
征、结构物附近三维水动力特征和波浪荷载，结合Boussinesq方程数值模型
和求解N-S方程的VOF方法各自的特点，开展了建立Boussinesq方程和N-
S方程耦合数值模型的研究。
整个研究工作包括以下几部分：
1）建立了有限差分全隐格式Boussinesq方程波浪数值模型。
全隐格式数值模型允许较小的网格尺度，计算过程稳定和结果收敛，并
能保证计算精度以及为与三维模型耦合求解时便于取得相匹配的网格尺
度。在开边界处理上，采取Sommerfeld辐射条件与海绵层吸收结合的
办法，较好地将到达开边界的波浪能量吸收掉。用所建立的Boussinesq
方程波浪数值模型进行了规则波在圆形浅滩上传播变形的数值计算，其
数值结果较好地接近于有关的实验结果，表明所开发的全隐格式
Boussinesq方程波浪数值模型是可靠的，以及具有较高的计算效率，可
以用于近岸大区域波浪变形的数值计算。
2）建立了基于N-S方程和VOF方法的三维数值波浪水池模型。
提出了用于VOF方法的分段式造波机边界条件，并对其它边界相应地给
出了合适的边界条件，建立了基于VOF方法的三维数值波浪水池。数值
试验表明，所提出的分段式造波机边界条件能够产生长时间稳定的波动
过程和斜入射波浪；对开边界的处理上采取了Sommerfeld辐射条件与
海绵层内衰减垂向速度相结合的处理方法，较好地使到达开边界的波浪
透过。数值试验表明所建立的数值波浪水池具有较好的波浪特性，并能
获得较为可靠的结构物波浪荷载结果。
论 丈 摘 要
一
3）建立了 ID Bousj NS－VOF＃合数值模型。
提出了重叠带上压力、速度和波面的匹配边界条件，建立了用二维川S方
程控制内域（包含结构物的近场）流体流动和一维Boussinesq方程控制
外域（内域的外围边界和整个计算域边界所围的区域）流体流动的耦合
数值模型（简称 ID／ZD耦合模型），在时间步进格式下，实现了内域模
型和外域模型同步耦合求解。数模试验显示本文提出的匹配边界条件能
够保证流动在这两个子区域之间光滑而连续地过渡，并且耦合模型模拟
结果（压力、速度、波面和波浪荷载）较好地接近于与原二维NS．VOF
模型的结果。
4）建立了二D BoussinesqoDNS－VOF耦合数值模型。
建立了用三维NS方程控制内域流体流动和二维Boussinesq方程控制
外域流体流动的部分三维化耦合数值模型（简称ZD／3D耦合模型）。数
模试验显示本文提出的压力、速度和波面匹配边界条件在斜人射波浪条
件下是有效性，能够保证流动在两个于区域之间光滑而连续地过渡；还
对耦合模型模拟波面和波浪荷载结果进行了验证，和对耦合模型的计算
效率进行了评估。
5）开展了耦合数值模型在工程数值计算上的觑。
·应用所建立的 ID／ZD耦合模型，进行了消减直立堤前反射波的幕墙
式消浪室性能的数模研究，得到了有意义的研究成果；
·应用所建立的 ZD／3D串联耦合模型对防彼堤堤头附近三维水动力特
征进行了初步研究，得到了有意义的研究成果；
·应用所建立的ZD／3D嵌套耦合模型对港内直立式码头前船舶波浪力
和船体附近三维水动力特征进行了初步研究，得到了有意义的研究
成果。
Abstract
As the depth-averaged simplification of the three-dimensional potential flow
model, the horizontal two-dimensional Boussinesq equations are suitable for
solving efficiently nonlinear wave propagation and transformation in large
shallow water regions (for example, harbor or coastal region with similar size).
On the other hand, because of depth-averaged simplification, the Boussinesq
equations can not be applied in solving such problems as wave actions on
submerged breakwaters, floating bodies etc., in which flow variations with depth
must be considered. For these problems, one must solve potential flow models or
viscous flow models, which are usually applied to a relatively small
computational region around the structure and not suitable for large fluid
domains, this is because both the 3D potential model and the 3D viscous model
are far more CPU time-consuming. Besides, all the flow features attached to
viscosity (vorticity, boundary layer) are disregarded in the modelling by potential
flow theory. One must solve viscous flow models to access these details of flow.
In order to obtain simultaneously and efficiently nonlinear wave
transformations in a harbor or coastal region, details of three dimensional flow
around structures and hydrodynamic loads of wave on marine structures,
combining advantages of Boussinesq model and NS-VOF model, we unfolded the
study of establishing Boussinesq / NS coupled numerical models.
The entire research work includes the following parts:
1) The Boussinesq equations numerical model with implicit differential
method is setup.
Numerical experiments reveal that the implicit method is accurate and
unconditional stable. The Sommerfeld radiation condition (SRC)
combined with sponge layer technique is applied at open boundaries, and
numerical tests verify the performance of SRC assisted by the sponge
layer technique. Computational results of regular waves propagating on a
circular shoal are in good agreement with the experimental data, showing
that the Boussinesq equation numerical model with implicit differential
method can give a satisfactory description of wave transformation over
the topography and can be applied in practical engineering.
2) The three dimensional numerical wave basin (NWB)based on 3D Navier-
Stokes equations and the VOF method is setup.
The wave maker boundary condition for the VOF method is proposed.
On other boundaries, in addition to reflection boundary conditions, the
open boundaries are treated by the technique of velocity reduction
zone(VRZ) at first, in which vertical velocity is reduced exponentially
inside the VRZ. Then Sommerfeld radiation condition is applied at the
open boundary. The performance of the present open boundary treatment
is verified by numerical experiments.
3) The 1D Boussinesq/2D NS-VOF coupled model is set up.
Matching boundary conditions for pressure, velocity and wave surface
elevation on the common matching boundary are proposed, and the
I D/2D coupled numerical model is setup, which is combination of the
2D NS-VOF model applied in the inner region (that is, the near-field
surrounding a marine structure), and the ID Boussinesq model applied in
the outer region. Numerical experiment shows that the present matching
boundary cond
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王永学(1989)．任意容器液体晃动问题的数学模型．大连理工大学博士学位论文
王永学，Su Tsung Chow(1991)．圆柱容器液体晃动问题的数值计算．空气动力学学报，9(1)：112～119
王永学(1993)．VOF方法数模直墙式建筑物前的波浪破碎过程．自然科学进展——国家重点实验室通讯，3(6)：553～559
王永学(1994)．无反射造波数值波浪水槽．水动力学研究与进展9(2)：205～214
王永学，任冰(1999)．波浪冲击过程的湍流数值模拟．水动力学研究与进展，A辑第14卷第4期：409～417
万德成，缪国平(1998)．数值模拟波浪翻越直立方柱．水动力学研究与进展，A辑第13卷第3期
徐本和(1996)．海岸和港口非线性波浪的数值模拟．大连理工大学硕士学位论文
邹志利(1997)．高阶Boussinesq水波方程．中国科学(E辑)，27(3)：460～473
邹志利(1999)．高阶Boussinesq水波方程的改进，中国科学(E辑)，29(1)：87～96