摆式波力电站中几个重要参数的设计

本文利用有限差分方法分析了摆式波力电中的摆板工作原理,建立了摆板运动方程的有限差分形式,通过计算机辅助设计,提出了一种最优化设计,包含有波浪力矩的推导,限位边界条件的考虑及最优化方程组。     

复杂地质体粘滞弹性波正演模拟的有限差分法

运用时空域的二阶中心差分法 ,由运动微分方程、自由边界条件及人工边界上的吸收边界条件 ,导出了二维非均匀粘滞弹性介质中波传播的二阶显示差分格式。该法可以方便且精确地处理自由表面、人工边界及交接层面。实现了在微机上用有限差分法对地震波在传播过程中的波型转换及波形变化的全波场模拟     

Finite difference analog of the Coriolis force in papers by Endoh

A wrong finite difference form is used for the rotation of the Coriolis force in the vorticity equation with bottom topography in a series of papers byEndoh.     

Approximate Variational Method for Ocean Data Assimilation

An approximate variational method is proposed to assimilate an oceanographic data set with a numerical ocean model. In the approximate method, the adjoint equation to a governing equation is derived and then converted to a finite difference form, in contrast to the ordinary, exact variational method which is composed of a finite difference equation adjoint to the finite difference governing equation. A cumbersome derivation of the adjoint equation is avoided, and finite difference schemes used for the original governing equation are easily utilized for the adjoint equation. This method has been verified with twin experiments. The flow field in the twin experiments is composed of dipole eddies in a two-layer quasi-geostrophic model. Initial and boundary conditions are control variables. The descent converges towards the exact field within 50 iterations, showing that the fundamental problem of the method (an unstable descent with a large number of iterations) does not appear. The approximate method is promising and should be tried with real data. This revised version was published online in July 2006 with corrections to the Cover Date.     

An integral contravariant formulation of the fully non-linear Boussinesq equations

In this paper we propose an integral form of the fully non-linear Boussinesq equations in contravariant formulation, in which Christoffel symbols are avoided, in order to simulate wave transformation phenomena, wave breaking and nearshore currents in computational domains representing the complex morphology of real coastal regions. Following the approach proposed by Chen (2006), the motion equations retain the term related to the approximation to the second order of the vertical vorticity. A new Upwind Weighted Essentially Non-Oscillatory scheme for the solution of the fully non-linear Boussinesq equations on generalised curvilinear coordinate systems is proposed. The equations are rearranged in order to solve them by a high resolution hybrid finite volume–finite difference scheme. The conservative part of the above-mentioned equations, consisting of the convective terms and the terms related to the free surface elevation, is discretised by a high-order shock-capturing finite volume scheme in which an exact Riemann solver is involved; dispersive terms and the term related to the approximation to the second order of the vertical vorticity are discretised by a cell-centred finite difference scheme. The shock-capturing method makes it possible to intrinsically model the wave breaking, therefore no additional terms are needed to take into account the breaking related energy dissipation in the surf zone. The model is verified against several benchmark tests, and the results are compared with experimental, theoretical and alternative numerical solutions.     

海洋水温垂直分布数据同化方法研究

以一维海洋水温模型为例,利用伴随法进行海洋观测数据同化试验,以便为水温的数值预报提供较准确的初始场.文中利用泛函的Gâteaux微分和Hilbert空间上伴随算子的概念讨论了连续的伴随模型的建立,并通过选择适当的差分格式离散伴随模型,使其保持连续时的伴随关系,同时给出了水温初始场最优化过程及相应的同化试验数值结果.     

Tidal flow near Mana Island,Cook Strait,New Zealand

Numerical calculations carried out for tidal flow on a small region of the New Zealand coast near Mana Island (41° 5 S, 174° 47 E) solved a finite difference form of the tidal equations, and assumed that the velocity boundary conditions could be approximated by a modified Kelvin wave formula. The results were exponentially smoothed in time at each step in the calculation to remove spurious modes.

The main results are shown as plots of tidal velocity vectors around Mana Island at equally spaced time intervals over a tidal cycle for one run commencing at low tide. The flow becomes very complex, with eddy shedding occurring in the wake of Mana Island, and a tidal rip developing across the shallow connection between Mana Island and the mainland.     

A hydrodynamic model of a two-part underwater towed system

A three-dimensional model of a two-part underwater towed system is studied. In the model, the governing equations of cables are established based on the Ablow and Schechter method. The boundary conditions for the two-part underwater towed system are derived. The six-degrees-of-freedom equations of motion for submarine simulations are adopted to predict the hydrodynamic performance of a towed vehicle. The established governing equations for the system are then solved using a central finite difference method. In this paper several algorithms are used to solve this special form of finite difference equations. The results in this paper indicate that the two-part underwater towed system improves the dynamic behavior of the towed vehicle and is an easy way to decouple the towing ship motion from the towed vehicle. Because the model uses an implicit time integration, it is stable for large time steps and is an effective algorithm for simulation of a large-scale underwater towed system.     

边界拟合坐标下流场计算模式

流场数值模拟中，采用曲线坐标法准确模拟计算水域自然边界情形是当今研究的热点之一。本文借助于自然界中某些物理现象中其函数符合椭圆型且必然正交这一特性，建立了曲线坐标系，弥补在笛卡尔坐标系下二维流场模拟的边界贴合不足。应用本模式对我国某一河口水域的潮位和流场进行计算，结果表明；该模式具有物理意义清晰、稳定性良好、精度高等特点，模式对实际工程中流场模拟具一定的应用价值。     

Implementation of method of lines to predict water levels due to a storm along the coastal region of Bangladesh

In this study, the method of lines (MOL) has been applied to solve two-dimensional vertically integrated shallow water equations in Cartesian coordinates for the prediction of water levels due to a storm surge along the coast of Bangladesh. In doing so, the partial derivatives with respect to the space variables were discretized by the finite difference (central) method to obtain a system of ordinary differential equations (ODEs) with time as independent variable. The classical fourth-order Runge–Kutta method was used to solve the obtained system of the ODEs. We used a nested finite difference scheme, where a high resolution fine grid model (FGM) capable of incorporating all major islands along the coastal region of Bangladesh was nested into a coarse grid model (CGM) covering up to 15°N latitude of the Bay of Bengal. The boundaries of the coast and islands were approximated through proper stair step. Appropriate tidal condition over the model domain was generated by forcing the sea level to be oscillatory with the constituent M ₂ along the southern open boundary of the CGM omitting wind stress. Along the northeast corner of the FGM, the Meghna River discharge was taken into account. The developed model was applied to estimate water levels along the coast of Bangladesh due to the interaction of tide and surge associated with the April 1991 storm. We also computed our results employing the standard finite difference method (FDM). Simulated results show the MOL performs well in comparison with the FDM with regard to CPU time and stability, and ensures conformity with observations.     

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.     

A finite volume discretization of the pressure gradient force using analytic integration

Layered ocean models can exhibit spurious thermobaric instability if the compressibility of sea water is not treated accurately enough. We find that previous solutions to this problem are inadequate for simulations of a changing climate. We propose a new discretization of the pressure gradient acceleration using the finite volume method. In this method, the pressure gradient acceleration is exhibited as the difference of the integral “contact” pressure acting on the edges of a finite volume. This integral “contact” pressure can be calculated analytically by choosing a tractable equation of state. The result is a discretization that has zero truncation error for an isothermal and isohaline layer and does not exhibit the spurious thermobaric instability.     

A Hybrid Finite-Volume and Finite Difference Scheme for Depth-Integrated Non-Hydrostatic Model

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.     

The second order spectrum of two-dimensional random waves

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Tides in the Tongan Region of the Pacific Ocean

Tidal levels and currents in the Tongan region of the Pacific were simulated using a two-dimensional frequency-domain finite element model. The eight major diurnal and semidiurnal tidal constituents were modeled successfully, using open boundary conditions taken from a global tidal model based on the Topex/Poseidon satellite altimeter. Comparison of model results with observations from the single tide gauge site in the area were later used to adjust the boundary conditions. The validity of omitting horizontal eddy viscosity from the finite element model was checked by running an equivalent finite difference model. The results show that although the submarine Tongan ridge does not appear to trap tidal energy, there are residual tidal currents and possible recirculations which are capable of influencing biological productivity around Tonga. The model results are reduced to a simple method for predicting tidal heights in outlying areas, based only on the tidal calendar for the capital, Nuku'alofa.     

Numerical modeling of multi-directional irregular waves incorporating 2-D numerical wave absorber and subgrid turbulence

In this paper, a finite difference scheme with an efficient 2-D numerical wave absorber for solving the extended Boussinesq equations as derived by Nwogu (Nwogu, O., 1993. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterway, Port, Coastal and Ocean Engineering, ASCE 119, 618–638) is proposed. The alternate direction iterative method combined with an efficient predictor-corrector scheme are adopted for the numerical solution of the governing differential equations. To parameterize the contribution of unresolved small-scale motions, the philosophy of the large eddy simulation is applied on the horizontal plane. The proposed method is verified by two test cases where experimental data are available for comparison. The first case is wave diffraction around a semi-infinite breakwater studied by Briggs et al. (Briggs, M.J., Thompson, E.F., Vincent, C.L., 1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE 121, 23–35). The other case is wave concentration by a navigation channel as reported by Yu et al. (Yu, Y.-X., Liu, S.-X., Li, Y.S., Wai, O.W.H., 2000. Refraction and diffraction of random waves through breakwater. Ocean Engineering 27, 489–509). Numerical results agree very well with the corresponding experimental data in both cases.     

地球流体中有限振幅波解的一般形式

从地球流体中非线性波动所的方程经行波变换所得的平面自治动力系统出发，利用微分方程几何理论，揭示了地球流体中几种非线性波动均具有周期解，而不存在孤波解的普遍性质，采用在平面自治系统的平衡点附近作Ｔａｙｌｏｒ展开方法，论述了分式简谐函数是有限振幅波解的一般形式的结论。     

Boussinesq-type modelling using an unstructured finite element technique

A model for solving the two-dimensional enhanced Boussinesq equations is presented. The model equations are discretised in space using an unstructured finite element technique. The standard Galerkin method with mixed interpolation is applied. The time discretisation is performed using an explicit three-step Taylor–Galerkin method. The model is extended to the surf and swash zone by inclusion of wave breaking and a moving boundary at the shoreline. Breaking is treated by an existing surface roller model, but a new procedure for the detection of the roller thickness is devised. The model is verified using four test cases and the results are compared with experimental data and results from an existing finite difference Boussinesq model.     

A Study on the Spectral Form of Nearshore Water Waves

- The spectral form of wind waves is investigated based on the ocean wave data observed at three nearshore stations of Taiwan. In this study, the generalized forms of Pierson-Moskowitz spectrum and JONSWAP spectrum are used to describe the local wave spectrum by selecting suitable spectral form parameters. It is shown that, at a specific site, the similarity of wave spectral form exists. Thus it is possible to use a representative spectral form for a given nearshore region to describe the wave spectrum at this nearshore. On the other hand, the effects of relative water depth on spectral form are examined. The feasibility of two spectral models in finite water depth is evaluated by using the same field wave data.     

Boussinesq水波方程新型数值解法

为建立高效的Boussinesq类水波数值模型,提出了一种新型的、基于有限差分和有限体积方法的混合数值格式。针对守恒形式的一维控制方程,在等间距矩形控制体内对其进行积分并离散,采用有限体积方法计算界面数值通量,剩余源项采用有限差分方法计算。其中,采用MUSTA格式并结合高精度状态插值方法计算控制体界面数值通量。时间积分则采用具有TVD性质的三阶龙格-库塔多步积分法进行。除验证模型外,重点对MUSTA格式和广泛使用的HLL格式进行了比较。结果表明,MUSTA格式可用于Boussinesq类水波方程数值求解,综合考虑数值精度、计算效率、程序编制和实际应用这几个方面,其较HLL格式更具有优势。