【作者】 佟飞飞；

【导师】 沈永明；

【作者基本信息】 大连理工大学 ， 港口、海岸及近海工程， 2010， 硕士

【摘要】 波浪以及破碎所产生的波生流场是近岸海域重要的水动力现象,是规划设计海岸工程,了解泥沙输运、海岸变形和近岸污染物扩散输移等近海问题的最基本因素。但是在近岸区域,地形和岸线往往比较复杂,采用规则矩形网格建模的常规方法易造成网格大小无法随地形变化,而且计算域边界与实际边界不吻合,从而增加计算量,并减少计算精度。而在实际工程中,工程师们通常更关心不规则岸线附近波浪和流场的分布,如河口、岛屿、码头和防波堤附近。本文的宗旨是建立一种适用于近海区域复杂地形和多变边界的数值模型,实现对近海区域水动力因素更精确的数值模拟。适体曲线坐标可以实现对曲折边界的无缝拟合,可以根据地形的变化调整网格的大小,而且曲线坐标转换一般不会对数值求解方法产生太大的影响,是目前计算流体力学中较为常见的处理复杂边界的数学方法。综合这些认识,本文基于坐标转换的基本理论,建立了正交曲线坐标系下的双曲型缓坡方程数值模型和基于缓坡方程的近岸波生流数值模型。首先,本文通过全面分析缓坡方程数学模型的研究进展,选择了数值计算方便,可以综合考虑波浪在大区域传播变形的两类双曲型模型作为控制方程,分别建立了正交曲线坐标系下的波浪数值模型。模型采用高效的ADI (Alternating Direction Implicit)有限差分法,进行离散求解。将所建立的波浪模型应用到若干个物理模型实验中,数值模拟的结果分别和实验值、理论解以及直角坐标系下的数值结果做了比较和分析；着重验证了模型对复杂地形和复杂边界、对扭曲的正交网格和对实际海域的适用性；本文还对两类双曲型缓坡方程的数值计算效率和精度做了适当的分析。本文通过波浪模型提供辐射应力等驱动力的概念,基于二维浅水方程建立了正交曲线坐标系下的近岸波生流数值模型。流场模型采用与波浪模型相同的正交网格和计算方法离散求解,即连续性方程采用隐格式,而动量方程交替采用显格式计算。应用所建立的波生流数值模型验证了波浪在曲线边界附近破碎产生沿岸流和裂流的情况,由波浪模型得到的辐射应力,通过源项的形式加入到流场模型中,为波流模型提供驱动力。通过物理模型实验验证结果表明,本文建立的基于缓坡方程的曲线坐标系下波流模型计算方便,可适用对复杂地形和多变边界地区波生流的数值计算。更多还原

【Abstract】 The nearshore waves and current induced by breaking waves are key hydrodynamic factors to coastal waters; understanding their rules of movement is the basic way to understand issues of the design of coastal projects, sediment transport, the deformation of coastlines and the diffusion of pollutants et al. However, the topography and coastline in the coastal regions are always complicated; therefore the conventional numerical modeling in rectangular grid could easily lead to the state that the boundary of computational domain does not match with the actual border, and thus reduce the accuracy of numerical results. While in practical engineering, engineers are usually more concerned about the distribution of waves and wave-induced current near irregular coastlines, such as, in the vicinity of estuaries, islands, piers and breakwaters.It is the object of this paper to establish a numerical model for coastal regions with complex terrain and variable boundaries, and to realize a more accurate hydrodynamic simulation of waves and current in these areas. Three reasons make the curvilinear coordinates transformation to be an outstanding mathematical method in dealing with complex boundary in fluid dynamics. They are being that firstly boundary-fitted grid can achieve a seamless fit to the curve border; secondly, the size of the grids can be adjusted according to changes in topography; and lastly coordinate transformation will not change the numerical method, in most cases. Based on this understanding, the present paper shows numerical models of the hyperbolic mild-slope equation and shallow water equation in orthogonal curvilinear coordinates.First of all, a comprehensive review of the development of nearshore wave modeling using the mild-slope equation was given. To facilitate numerical calculation, two different hyperbolic approximations of mild-slope equation, which are capable to describe wave transformation in large areas, were chosen to study under orthogonal curvilinear coordinates. The established wave models were discreted with a space-staggered grid and solved by the efficient ADI method (Alternating Direction Implicit).Then, wave models were applied to several physical experiments; the numerical results were compared to experimental data, analytical results, and numerical results from Cartesian coordinates, available. The numerical models were validated by their applicability to the complicated terrain and boundaries, to the distortion of orthogonal grids, and to the practical engineering application. Appropriate analysis was also given on the numerical accuracy and efficiency of the two kinds of hyperbolic mild-slope equations.Thirdly, the two-dimensional shallow water equations were transformed in orthogonal curvilinear coordinates based on the concept of the radiation stress theory. The numerical solving method of the transform current model was the same as wave model, i.e., the continuity equation being calculated by the implicit scheme and the momentum equations by alternating explicit scheme.Last but not the least, the regular wave-induced longshore currents and rip currents were calculated through the transformed current model. Here, the established hyperbolic mild-slope wave model was employed as a driving force to flow field. The good agreement of numerical results with experimental data and with published numerical results showed that the numerical model in this paper is applicable to simulate wave-induced current in areas with complicated topography and boundary conditions.更多还原