浅水波方程的TVD有限差分数值模拟

本文将Harten的总变差缩减有限差分格式(TVD),应用于非线性的不可压缩的浅水波方程数值求解。通过对一锥、二维溃坝洪水波的数值模拟,成功地模拟了溃坝问题中的激波和膨胀波现象,保持了解在间断处陡峭,而在其两侧无振动。     

交替蛙跳格式在POM的应用

讨论交替蛙跳格式在二维POM的运用。这个交替蛙跳格式是在z坐标下开发的针对线性浅水波方程的一种新的高效无耗散的格式。首先通过一维问题的试验,给出了σ坐标下非线性浅水波的演化特性及其交替蛙跳格式的数值特性,证实该格式的可行性以及优于传统格式的计算效率、守恒性及稳定性。其次,针对该格式二维问题运用讨论了科氏项相应的数值处理,给出了一套完整的数值计算方法,并应用于正压方程和POM外模的数值计算。研究表明,交替蛙跳格式具有两倍于传统蛙跳格式的计算效率,且不再需要Assenlin时间滤波,由此避开了时间滤波带来的数值衰减,具有良好的数值守恒性能。     

基于WENO格式的高精度高分辨台风风暴潮数值模式

考虑到台风风暴潮在近岸浅水地区的非线性效应,基于无结构网格,通过采用有限体积法和高精度高分辨率的WENO数值格式对二维浅水方程进行空间离散,并利用三阶的Runge-Kutta格式进行时间离散,最后利用Rogers方法解决复杂海底地形造成的通量梯度项与源项数值离散后的不平衡问题,从而建立了二维台风风暴潮数值模式。模式中的风场和气压场分别采用宫崎正卫风场模式和藤田气压场模式。最后通过对江苏沿海的风暴增水的模拟和验证,表明了该数值模式对台风风暴潮模拟的有效性和可行性。     

近岸二维海流数值计算方法若干问题的研究和应用

就二维浅水流体动力方程应用物理意义明确的有限体积法，收敛快而稳定的五对角全隐格式，以及嵌套、变步长的网格和动边界技术，进行二维海流场的数值计算，并研究了开边界为斜断面的定解条件的数值方法和开边界上断面各点水位的计算方法。最后把本数值方法应用于某海岸工程的可行性研究，并验证了这种海流数值计算方法的合理性。     

浅水动力学的格子Boltzmann模拟

建立了一个格子Boltzmann模型,经过Chapman-Enskog展开可以恢复出守恒形式的浅水动力学方程组。理论分析和数值试验的结果都表明,本模型严格地满足质量守恒定律和动量定理。数值模拟了一维和二维溃坝流动,分别与理论解和文献值进行了对比,结果相当吻合。本模型具有很好的并行计算性能,在海洋、大气等大规模数值计算领域有着广阔的发展前景。     

近岸二维海流数值计算方法若干问题的研究和应用

就二维浅水体动力方程应用物理意义明确的有限体积法，收敛快而稳定的五对角全隐格式，以及嵌套，变步长的网格和动边界技术，进行二维海流场的数值计算，并研究了开边界为斜断面的定解条件的数值方法和开边界上断面各点水位的计算方法。最后把本数值方法应用于某海岸工程的可行性研究，并验证了这种海流数值计算方法的合理性。     

防潮闸启闭影响下的河口水流泥沙运动状态研究

为研究防潮闸启闭与跨水工程建设对河口地区水流泥沙运动状态的影响,以河口近闸跨水工程为背景,建立了以Godunov格式有限体积法为基础的二维浅水流动数学模型和基于固液二相流理论的二维水流泥沙数学模型,并以实测资料进行必要验证,结果较为吻合。在此基础上,建立了永定新河河口区域二维水沙数值模型,将该模型应用于滨海新区Z4线一期跨河工程段的水沙分析,并对工程建设后永定新河河口水流泥沙运动的变化趋势进行预报。结果表明永定新河河口二维全沙模型较为可靠,可为河口近闸跨水工程的相关分析提供研究思路和方法。     

二维非线性浅水波的数值模拟

研究工作的目的在于建立一个能够模拟二维潮流、洪水波(长波)和浅水波浪(短波)的综合数学模型.基本模型建立在非线性的Boussinesq方程基础之上.本文主要讨论浅水波浪即短波的数值模拟.模型可以考虑必要的外力项,如柯氏力、风应力、大气压力和底摩阻力等.针对Boussinesq方程提出了一个全隐的二维差分格式,讨论了人工开边界的处理方法.模型被用来计算了突然扩张渠槽中的环流和单突堤后的水波绕射,取得了满意的结果.     

解Burgers方程的迎风加权交替分块显-隐方法

利用迎风加权格式对二维Burgers方程的对流项进行处理,构造求解二维Burgers方程的一类交替分块显隐的有限差分格式,该方法具有并行本性,且绝对稳定.数值实验表明方法还具有较好的精度.     

基于物理造波和主动消波的黏性数值波浪水槽开发

基于推板造波理论和摇板造波理论,在Open FOAM平台上采用重叠网格技术建立黏性数值波浪水槽,并使用一种结合SIMPLE算法和PISO算法的PIMPLE算法对数值模型进行求解。利用开发的数值模型通过数值收敛性测试和网格独立性测试分别重点研究了时间步长、库朗数和网格尺寸对数值精度和计算效率的影响。并对比研究了此数值模型分别嵌入层流模型和湍流模型的计算精度和计算效率。实现的规则波和二阶有限振幅波与理论结果和试验结果吻合,验证了此黏性数值波浪水槽的造波和主动消波功能。基于二维数值波浪水槽,进一步研究了三维数值造波,数值计算结果与理论结果吻合良好。研究结果不仅验证了重叠网格在二维和三维两相流体域中求解运动物体与流场交互的可靠性和正确性,而且为使用此黏性数值波浪水槽解决更复杂的海洋工程问题提供了依据。     

High-resolution central difference scheme for the shallow water equations

1 IntroductionThe shallow water equations (SWE) are frequent-ly used as a mathematical model for water flows incoastal areas, lakes, estuaries, etc. Thus, they are animportant tool to simulate a variety of problems relat-ed to coastal engineering, environment, ecology, etc.(Bermúdez et al., 1998). On the basis of solving theone-dimensional (1D) SWE, Hu et al. (2000) have de-veloped a model capable of simulating storm wavespropagating in the coastal surf zone and overtopping asea wall. Ano…     

A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.     

An Application of Finite Volume WENO Scheme to Numerical Modeling of Tidal Current

1 .IntroductionThe development and application of hydrodynamic models to predict circulation in estuarine ,coastal ,and shelf waters has been extremely active over the past three decades (Spauldinget al .,1992 ,1994) . However , most of these models are b…     

On the numerical modeling of tsunami wave generation and propagation

Abstract

In this article three main stages of tsunami wave evolution are investigated. At first, the development of disturbances from a given patched elevation of the bottom surface in an incompressible nonviscous fluid of the uniform depth is considered. Then, a tsunami wave diffraction by underwater bottom elevation or cavity is investigated. In this case the shallow water equations are already used, and it is supposed that a cylindrical wave is spread from patched water elevation over the epicentrum. Last, the tsunami propagation and transformation in a shallow water region and its run‐up on a beach are investigated on the basis of the improved shallow water theory, taking into consideration the nonlinear and dispersive terms of higher order. The proposed theory is tested in a problem of collisions of two solutions. Solutions of the first and the second problems are obtained by the method of integral Laplace's transformation with following numerical inversion of transformations. A finite difference method for a solution of the last problem is used.     

Numerical Study of Dam-Break Induced Tsunami-Like Bore with A Hump of Different Slopes

Numerical simulation of dam-break wave, as an imitation of tsunami hydraulic bore, with a hump of different slopes is performed in this paper using an in-house code, named a Constrained Interpolation Profile (CIP)-based model. The model is built on a Cartesian grid system with the Navier Stokes equations using a CIP method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of solid body boundary. A more accurate interface capturing scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) scheme, is adopted as the interface capturing method. Then, the CIP-based model is applied to simulate the dam break flow problem in a bumpy channel. Considerable attention is paid to the spilling type reflected bore, the following spilling type wave breaking, free surface profiles and water level variations over time. Computations are compared with available experimental data and other numerical results quantitatively and qualitatively. Further investigation is conducted to analyze the influence of variable slopes on the flow features of the tsunami-like bore.     

Wave transformation by axisymmetric three-dimensional bathymetric anomalies with gradual transitions in depth

The development of an analytic model (Axisymmetric 3-D Step Model) for the propagation of linear water waves over an axisymmetric bathymetric anomaly in arbitrary water depth is presented. The Axisymmetric 3-D Step Model is valid in a region of uniform depth containing an axisymmetric bathymetric anomaly with gradual transitions in depth allowed as a series of steps approximating arbitrary slopes. The velocity potential is calculated by applying matching conditions at the interface between regions of constant depth. The velocity potential obtained determines the wave field in the domain for monochromatic incident waves of linear form. A second analytic model (3-D Shallow Water Exact Model) is developed for comparison within the shallow water limit.The Axisymmetric 3-D Step Model determines the wave transformation caused by the processes of wave refraction, diffraction and reflection. Wave transformation is demonstrated in plots of the relative amplitude for bathymetric anomalies in the form of pit or a shoal, highlighting areas of wave sheltering and wave focusing. Anomalies of constant volume, but variable cross-section are employed to isolate the effect of the transition slope on the wave transformation.Comparisons to a shallow water model, numerical models, and experimental data verify the results of the Axisymmetric 3-D Step Model for several bathymetries including both pits and shoals. Also included are estimates of the energy reflection induced by an axisymmetric depth anomaly. The 3-D Axisymmetric Step Model has been applied previously to account for nearshore transformation (sloping bathymetry) and associated shoreline changes [C.J. Bender, R.G. Dean, Coastal Engineering 51 (2004) 1143].     

Fast computation of the transient motions of moving vessels in irregular ocean waves

A fast time-domain method is developed in this paper for the real-time prediction of the six degree of freedom motions of a vessel traveling in an irregular seaway in infinitely deep water. The fully coupled unsteady ship motion problem is solved by time-stepping the linearized boundary conditions on both the free surface and body surface. A velocity-based boundary integral method is then used to solve the Laplace equation at every time step for the fluid kinematics, while a scalar integral equation is solved for the total fluid pressure. The boundary integral equations are applied to both the physical fluid domain outside the body and a fictitious fluid region inside the body, enabling use of the fast Fourier transform method to evaluate the free surface integrals. The computational efficiency of the scheme is further improved through use of the method of images to eliminate source singularities on the free surface while retaining vortex/dipole singularities that decay more rapidly in space. The resulting numerical algorithm runs 2–3 times faster than real time on a standard desktop computer. Numerical predictions are compared to prior published results for the transient motions of a hemisphere and laboratory measurements of the motions of a free running vessel in oblique waves with good agreement.     

Wave diffraction by large offshore structures: an exact second-order theory

An exact second order theory has been formulated in this paper to calculate the wave forces on offshore structures. Lighthill's method for deep water waves has been extended to shallow water waves. Exact expression for linear velocity potential applicable to the circular cylindrical strcutures for shallow water waves have been used in these calculations. These results have been verified with those obtained by direct perturbation technique reported recently by Rahman and Heaps. It is interesting to note that both the methods yield identical results.     

Linearised water wave problems involving submerged horizontal plates

In this paper a number of related linearised water wave problems all involving thin submerged horizontal plates are considered. An integral transform approach is adopted and used to formulate integral equations in terms of unknown functions related to the jump in pressure across the plate. A Galerkin method is applied to the solution of these integral equations leading to elegant expressions for quantities of interest and a rapidly convergent numerical scheme. The focus of the paper is to demonstrate the application of this method in a number of settings including both two-dimensional problems applied to infinitely-long plates of constant width and three-dimensional problems involving circular discs. In the process we present new results including, for example, for wave-free forced oscillations of plates.     

Validation of the three-wave quasi-kinetic approximation for the spectral evolution in shallow water

This paper aims at validating the three-wave quasi-kinetic approximation for the spectral evolution of weakly nonlinear gravity waves in shallow water. The problem is investigated using a one-dimensional numerical wave propagation model, formulated in the spectral representation. This model includes both a nonlinear triad interactions term and a wave breaking dissipation term. Some numerical tests were carried out in order to show the importance of using the triad nonlinear term in wave propagation spectral models, particularly to describe both behavior of the spectral integral parameters and of the spectral shape evolution in shallow water depth. Furthermore; a comparison against different set of experimental observations was carried out. Comparing the numerical results with the experimental observations made it possible to show the modeling efficiency of the three-wave quasi-kinetic approximation.