共查询到20条相似文献，搜索用时 15 毫秒
1.
《Coastal Engineering》2004,51(1):17-34
Approximate equations for the elliptic mild slope equation are derived based on Padé approximation and used as absorbing boundaries. The new boundary equations can absorb the incident waves for high range of wave incidence angle. In addition, the new boundary equations can be used iteratively to refine the solution by eliminating reflections from the boundaries. An iterative conjugate gradient scheme has been used to solve the elliptic water wave equation and the new boundary equations. The model developed can accommodate for wave diffraction, refraction and reflections from structures with wide range of wave angles at the boundaries. The new model has been tested for several cases. The model compares very well with other models. 相似文献
2.
《Coastal Engineering》2005,52(6):513-533
Using the perturbation method, a time dependent parabolic equation is developed based on the elliptic mild slope equation with dissipation term. With the time dependent parabolic equation employed as the governing equation, a numerical model for wave propagation including dissipation term in water of slowly varying topography is presented in curvilinear coordinates. In the model, the self-adaptive grid generation method is employed to generate a boundary-fitted and varying spacing mesh. The numerical tests show that the effects of dissipation term should be taken into account if the distance of wave propagation is large, and that the outgoing boundary conditions can be treated more effectively by introduction of the dissipation term into the numerical model. The numerical model is able to give good results of simulating wave propagation for waters of complicatedly boundaries and effectively predict physical processes of wave propagation. Moreover, the errors of the analytical solution deduced by Kirby et al. (1994) [Kirby, J.T., Dalrymple, R.A., Kabu, H., 1994. Parabolic approximation for water waves in conformal coordinate systems. Coastal Engineering 23, 185–213.] from the small-angle parabolic approximation of the mild-slope equation for the case of waves between diverging breakwaters in a polar coordinate system are corrected. 相似文献
3.
波浪在斜坡地形上破碎,破波后稳定波高多采用物理模型试验方法进行研究,利用近岸波浪传播变形的抛物型缓坡方程和波能流平衡方程,导出了适用于斜坡上波浪破碎的数值模拟方法。首先根据波能流平衡方程和缓坡方程基本型式分析波浪在破波带内的波能变化和衰减率,推导了波浪传播模型中波能衰减因子和破波能量流衰减因子之间的关系;其次,利用陡坡地形上的高阶抛物型缓坡方程建立了波浪传播和波浪破碎数学模型;最后,根据物理模型试验实测数据对数值模拟的效果进行验证。数值计算与试验资料比较表明,该模型可以较好地模拟斜坡地形的波浪传播波高变化。 相似文献
4.
《Coastal Engineering》2006,53(4):319-323
The literature contains empirical knowledge on whether the wave celerity or the group velocity should be used in the line source function for internal wave generation for at given set of Boussinesq or mild-slope equations. Theoretical derivations that confirm and explain these empirical findings are devised. For Boussinesq equations with, e.g. Padé[2,2]-type of dispersion relation some procedures for internal wave generation are affected by their excitation of an evanescent mode. This has some undesirable consequences, but the evanescent-mode excitation can be avoided by the use of an “internal flux boundary”. 相似文献
5.
《Coastal Engineering》2005,52(5):391-407
A numerical solver is presented of the modified time-independent mild-slope equation, which incorporates energy dissipation. Using a second-order parabolic approximation, the following external boundary conditions are modelled: open and fully transmitting to both incoming and outgoing waves; partially reflecting, and; fully absorbing. Discretisation of the governing equation and boundary conditions is by means of a second-order accurate central difference scheme. The resulting sparse-banded matrix is solved using an inexpensive banded solver with Gaussian elimination. The numerical predictions are in excellent agreement with the analytical solution for the interaction of non-breaking waves with an array of vertical surface-piercing circular cylinders on a horizontal bed. Results are compared with those for the same array on various seabed topographies. The model is robust and can be used for wave propagation in complex geometries. It has fewer restrictions associated with wave obliqueness at boundaries than traditional models based on the mild-slope equation. 相似文献
6.
Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results. 相似文献
7.
Wave-Current Propagation over a Frictional Topography 总被引：1，自引：0，他引：1
ZUO Qihua DING Bingcan Prof. Senior Engineer River Harbour Department Nanjing Hydraulic Research Institute 《中国海洋工程》1998,(4)
—In this paper the parabolic approximation model based on mild-slope equation is used tostudy wave propagation over a slowly varying and frictional topography under wave-current interaction.A governing equation considering the friction effects is derived by the authors for the first time.A simpli-fied form for the rate of wave energy dissipation is presented on the basis of the wave-current action conser-vation equation and the bottom friction model given by Yoo and O＇connor(1987).Examples reveal thatthe present computational method can be used for the calculation of wave elements for actual engineeringprojects with large water areas. 相似文献
8.
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based on Born approximation. 相似文献
9.
将适用于近岸较大区域波浪传播变形的三种模型,即基于抛物型缓坡方程的不规则波模型、引入浅水波浪谱 TMA 谱的 SWAN(simulating waves nearshore)模型以及采用默认 JONSWAP 谱的 SWAN模型应用于特拉华大学(University of Delaware)圆形浅滩实验进行比较.结果显示,抛物型缓坡方程和SWAN 的模拟结果与实验所测数据符合都比较好; SWAN 在非线性作用较强的浅滩中心及靠后部效果更佳,而抛物型缓坡方程由于没有考虑非线性作用,模拟得到的最大波高较实测值偏高,且波高变化较为剧烈. 相似文献
10.
Parabolic Approximation of the Weakly Nonlinear Mild Slope Equation with Bottom Friction 总被引：2，自引：0，他引：2
This paper presents a refined parabolic approximation model of the mild slope equation to simu-late the combination of water wave refraction and diffraction in the large coastal region.The bottom frictionand weakly nonlinear term are included in the model.The difference equation is established with the Crank-Nicolson scheme.The numerical test shows that some numerical prediction results will be inaccurate in com-plicated topography without considering weak nonlinearity;the bottom friction will make wave height damp-ing and it can not be neglected for calculation of wave field in large areas. 相似文献
11.
Dobrovol'skaya [1] presented a similarity solution for the water entry of symmetrical wedges with constant velocity. The solution involves an integral equation that becomes increasingly harder to numerically solve as the deadrise angle decreases. Zhao and Faltinsen [2] were able to present reliable results for deadrise angles down to 4°. In this paper, Zhao and Faltinsen's results are improved and reliable results for deadrise angles down to 1° are confirmed by comparing to the asymptotic solutions at small deadrise angles and the solutions by the traditional boundary element method at relatively large deadrise angles. The present similarity solution results provide a reference solution in theoretical studies of water entry problems and in developing accurate numerical solvers for simulating strongly nonlinear wave–body interactions, which flows are governed by Laplace equation or Euler equation. 相似文献
12.
James T. Kirby 《Coastal Engineering》1986,10(4)
Approximations based on minimax principles are developed in order to allow for large-angle propagation in the parabolic equation method. Numerical studies show that the minimax approximations do not cause any significant degradation of accuracy at small angles of incidence when compared with an existing model based on a (1,1) Padé approximant, and that they allow for much more successful treatment of large angles of incidence than is possible using the previously available methods. 相似文献
13.
Induced swell is characterized in an experimental wave flume that is used to validate the corresponding computational model. The experiments and the numerical simulations are performed in water at several depths (h [m] of 0.2, 0.1, and 0.07), using a piston-type wave maker at set amplitudes (0.015 < Ap [m] < 0.15), accelerations-decelerations (0.3 < ap < 1.0) and average velocities (0.03 < U [m/s] < 0.3) that control the propagation velocity, the period and the wavelength of the waves. The physical effects are modelled with a 2D computational model (STAR-CCM + v11.02) with a mesh of around 630,000 cells of different adaptive sizes, depending on the region under consideration. The physical model is based on a two-phase Eulerian “Volume of Fluid” unsteady model, accounting for gravity and surface tension, that characterizes turbulence with a k-ε model. A user-defined function, based on the period and the amplitude of the vertical paddle in the wave maker, describes the cyclic motion of the linear induction motor. Both the experimental and the computational results are analyzed taking the validity limits of various wave theories as a reference (Le Méhauté). As a result, the experiments are classified within the intermediate water depth regime that corresponds to the second-order Stokes’ wave theory. In addition, both the wave propagation velocity and the period are represented as a function of the wavelength and compared with the analytical solutions from the wave theories. The experimental and the computational test campaign yielded results that confirmed the validity of the computational model and that defined the most appropriate conditions for a high-quality CFD simulation. 相似文献
14.
The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary conditions. With wave breaking and energy dissipation expressed in a direct form in the equation, the proposed model could provide an efficient numerical scheme and accurate predictions of wave transformation across the surf zone. The radiation boundary conditions are iterated in the model without use of approximations. The numerical predictions for wave height distributions across the surf zone are compared with experimental data over typical beach profiles. In addition, tests of waves scattering around a circular pile show that the proposed model could also provide reasonable improvement on the radiation boundary conditions for large incident angles of waves. 相似文献
15.
Spectral wave transformation model for simulating refraction-diffraction with strongly reflecting coastal structures 总被引：1，自引：0，他引：1
On the basis of the wave action balance equation which incorporates refraction, diffraction, reflection and wave-current interaction, a directional spectral wave transformation model WABED is developed for predicting the irregular wave refraction-diffraction with strongly reflecting structures in coastal regions. In the model, diffraction is taken into account by introducing a term formulated from a parabolic approximation wave equation, and reflection is calculated through a back-marching numerical approach at the reflecting boundary. Two experimental data sets are used to examine the performance of present model with regard to wave characteristics around reflecting coastal structures. One is from a physical experiment at idealized inlet with parallel jetties, while the other is from a laboratory study on a coastal project of the concave breakwater. Reasonably good agreements are found for both cases, revealing the applicability of the present model for predicting combined wave refraction-diffraction processes with strongly reflecting coastal structures. 相似文献
16.
Hong-Sheng Zhang Hong-Jun Zhao Ping-Xing Ding Guo-Ping Miao 《Ocean Engineering》2007,34(10):1393-1404
By transforming two different time-dependent hyperbolic mild slope equations with dissipation term for wave propagation on non-uniform currents into wave-action conservation equation and eikonal equation, respectively, shown are the different effects of dissipation term on the eikonal equation in the two different mild slope equations. The performances of intrinsic frequency and wave number are also discussed. Thus the suitable mathematical model is chosen in which the wave number vector and intrinsic frequency are expressed both more rigorously and completely. By using the perturbation method, an extended evolution equation, which is of time-dependent parabolic type, is developed from the time-dependent hyperbolic mild slope equation which exists in the suitable mathematical model, and solved by using the alternating direction implicit (ADI) method. Presented is the numerical model for wave propagation and transformation on non-uniform currents in water of slowly varying topography. From the comparisons of the numerical solutions with the theoretical solutions of two examples of wave propagation, respectively, the results show that the numerical solutions are in good agreement with the exact ones. Calculating the interactions between incident wave and current on a sloping beach [Arthur, R.S., 1950. Refraction of shallow water waves. The combined effects of currents and underwater topography. EOS Transactions, August 31, 549–552], the differences of wave number vector between refraction and combined refraction–diffraction of waves are discussed quantitatively, while the effects of different methods of calculating wave number vector on numerical results are shown. 相似文献
17.
TAO Jianhua 《中国海洋工程》2001,(2):269-280
The "surface roller" to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation including diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circular shoal, and the numerical results of random wave breaking model agree with the experimental data very well. This model can be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natu ral topography. 相似文献
18.
A mode-splitting method is applied to the quasi-3D nearshore circulation equations in generalized curvilinear coordinates. The gravity wave mode and the vorticity wave mode of the equations are derived using the two-step projection method. Using an implicit algorithm for the gravity mode and an explicit algorithm for the vorticity mode, we combine the two modes to derive a mixed difference–differential equation with respect to surface elevation. McKee et al.'s [McKee, S., Wall, D.P., and Wilson, S.K., 1996. An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms. J. Comput. Phys., 126, 64–76.] ADI scheme is then used to solve the parabolic-type equation in dealing with the mixed derivative and convective terms from the curvilinear coordinate transformation. Good convergence rates are found in two typical cases which represent respectively the motions dominated by the gravity mode and the vorticity mode. Time step limitations imposed by the vorticity convective Courant number in vorticity-mode-dominant cases are discussed. Model efficiency and accuracy are verified in model application to tidal current simulations in San Francisco Bight. 相似文献
19.
Three models were applied to analyse the planform of bay-shaped Portuguese beaches. They are based on empirical mathematical functions: the logarithmic spiral bay equation, the hyperbolic-tangent bay equation, and the parabolic bay equation. These models were applied to analyse the fitting to the beach planform of 42 beaches on the Portuguese Atlantic coast which was calculated through the validation against the waterline extracted from rectified aerial photographs. The logarithmic spiral model fits well the curved zone of the beaches, in particular small beaches with two headlands. Despite the good fitting of the hyperbolic-tangent model for one headland beach, its process of approximation to the solution was less intuitive than the processes of the other two models, therefore its application was more exhaustive. A comparative analysis between the logarithmic spiral model and the hyperbolic-tangent model revealed the best fit of the first. The application of the parabolic model allowed to conclude that despite the majority of the beaches analysed being in dynamic equilibrium condition due to the high energy wave regime of the Portuguese Atlantic coast, their planform was very close to the planform in static equilibrium condition due to the high dynamics of the coastal environment. 相似文献
20.
An obvious motivation of this paper is to examine the effectiveness of the lateral vibration control of a jacket type offshore platform with an AMD control device, in conjunction with H2 control algorithm, which is an optimal frequency domain control method based on minimization of H2 norm of the system transfer function. In this study, the offshore platform is modeled numerically by use of the finite element method, instead of a lumped mass model. This structural model is later simplified to be single-degree-of-freedom (SDOF) system by extracting the first vibration mode of the structure. The corresponding "generalized" wave force is determined based on an analytical approximation of the first mode shape function, the physical wave loading being calculated from the linearized Morison equation. This approach facilitates the filter design for the generalized force. Furthermore, the present paper also intends to make numerical comparison between H2 active control and the corresponding passive control using a T 相似文献