基于CFD的风生波浪的数值模拟

发布时间：2018-03-27 12:00

本文选题：SWAN　切入点：扩展的双曲型缓坡方程　出处：《杭州电子科技大学》2014年硕士论文

【摘要】：近岸波浪传播变形的模拟是水动力学研究的一项重要内容，而风生波浪往往是其最基本的产生形式。波浪的风生机制仍未得到有效解决，近岸波浪传播变形的模拟也涉及到大量动力机制，十分复杂。风生波浪的数值模拟问题含以上两方面的难点，需结合多个波浪模型方可进行有效求解。SWAN模型在刻画波浪风生机制及波-波相互作用方面优势明显；本文建立的扩展双曲型缓坡方程在描述波浪在复杂地形上的传播变形问题时不仅可以考虑波浪的联合折射、绕射、反射和浅化效应，而且能够通过添加的修正项计及水底快速变化地形的二阶因子的影响、波浪非线性色散效应、风能输入、底摩阻耗散和波浪破碎耗散。因此，对于风起主导作用地形上波浪的传播变形问题，联合以上两个波浪模型，，使之既能精确考虑波浪的风生机制又能反映出近岸复杂地形和建筑物的影响。本文首先从流体力学理论出发回顾了风生波浪问题的由来，阐述风生波浪数值模拟的两大难题（风生机制和传播变形）及其各自数学模型的发展，尤其是CFD的出现给问题的求解带来了便利条件。通过分析各个波浪数值模拟模型的优缺点，第二部分给出了缓坡方程和SWAN模型的详细说明。Berkhoff缓坡方程为一椭圆型方程，能够刻画波浪联合折射、绕射、反射作用，经过扩展已能够考虑更多的动力机制，经过改进发展出抛物型缓坡方程与双曲型形缓坡方程。基于动谱平衡方程的SWAN模型，以源汇项线性叠加的方式来考虑各种物理机制，对风生机制处理上比较精确。本文第三部分在考虑流作用的缓坡方程基础上，建立了一个扩展的双曲型缓坡方程，给出了具体的边界条件，提出了ADI格式与C-N格式相结合的数值求解方法。针对辐射边界条件中波向不确定问题，给出了沿空间推进的麦考马克（MacCorMack）预估-校正的方法来求解波数矢无旋方程，从而得到计算域内波向。第四部分选用了四个典型试验地形对该扩展方程的适用性进行了验证，给出了原双曲型方程、扩展方程的计算结果与试验值之间的对比，证明了本扩展模型的有效性。对于风生波浪的数值模拟，第五部分我们给出了一个SWAN自嵌套和扩展双曲型缓坡方程联合使用的方案，综合利用了SWAN在刻画风生机制和波-波作用上的合理性和扩展模型在描述波浪传播变形方面的固有优势。
[Abstract]:Simulation of wave propagation and deformation near shore is an important part of hydrodynamic research, and wind-induced wave is often the most basic form of wave generation. The wind-induced mechanism of wave has not been solved effectively. The simulation of wave propagation and deformation near shore also involves a large number of dynamic mechanisms and is very complicated. The numerical simulation of wind-induced waves involves the difficulties mentioned above. In order to solve the SWAN model effectively, it is necessary to combine several wave models in order to describe the wind-induced mechanism and wave-wave interaction. The extended hyperbolic gentle slope equation in this paper can not only consider the joint refraction, diffraction, reflection and shallowness of waves in describing the propagation and deformation of waves on complex terrain. Furthermore, it is possible to take into account the influence of second-order factors of rapidly changing topography under the water bottom, wave nonlinear dispersion effect, wind energy input, bottom friction dissipation and wave breaking dissipation by adding correction items. For the problem of wave propagation and deformation in the dominant terrain, the above two wave models are combined to accurately consider the wind-induced mechanism of waves and to reflect the influence of complex landforms and buildings on the shore. In this paper, the origin of wind-induced wave problem is reviewed based on the theory of hydrodynamics, and the development of two difficult problems (wind-induced mechanism and propagation deformation) and their respective mathematical models are expounded. Especially, the appearance of CFD brings convenience to the solution of the problem. By analyzing the advantages and disadvantages of each wave numerical simulation model, the second part gives the detailed description of the gentle slope equation and the SWAN model. The Berkhoff gentle slope equation is an elliptic equation. It can depict the combined refraction, diffraction and reflection of waves. By extension, it has been able to take into account more dynamic mechanisms, and the parabolic gentle slope equation and hyperbolic gentle slope equation have been developed through improvement. The SWAN model based on the dynamic spectrum equilibrium equation has been developed. In the third part of this paper, an extended hyperbolic gentle slope equation is established on the basis of the gentle slope equation considering the flow action. In this paper, the concrete boundary conditions are given, and a numerical solution method combining ADI scheme and C-N scheme is proposed. In this paper, a method of predictor-correction of MacCorMack-Propulsion along the space is presented to solve the wavenumber vector equations, and the wave directions in the domain are obtained. In the fourth part, the applicability of the extended equation is verified by the selection of four typical experimental terrain. The comparison between the calculated results of the original hyperbolic equation and the experimental data proves the validity of the extended model. In the fifth part, we give a scheme of SWAN self-nesting and extended hyperbolic gentle slope equation. The rationality of SWAN in describing wind-induced mechanism and wave-wave interaction and the inherent advantages of the extended model in describing wave propagation and deformation are comprehensively utilized.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P731.22

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