本文選題：SWAN　切入點：擴展的雙曲型緩坡方程　出處：《杭州電子科技大學》2014年碩士論文

【摘要】：近岸波浪傳播變形的模擬是水動力學研究的一項重要內(nèi)容，而風生波浪往往是其最基本的產(chǎn)生形式。波浪的風生機制仍未得到有效解決，近岸波浪傳播變形的模擬也涉及到大量動力機制，十分復雜。風生波浪的數(shù)值模擬問題含以上兩方面的難點，需結合多個波浪模型方可進行有效求解。SWAN模型在刻畫波浪風生機制及波-波相互作用方面優(yōu)勢明顯；本文建立的擴展雙曲型緩坡方程在描述波浪在復雜地形上的傳播變形問題時不僅可以考慮波浪的聯(lián)合折射、繞射、反射和淺化效應，而且能夠通過添加的修正項計及水底快速變化地形的二階因子的影響、波浪非線性色散效應、風能輸入、底摩阻耗散和波浪破碎耗散。因此，對于風起主導作用地形上波浪的傳播變形問題，聯(lián)合以上兩個波浪模型，，使之既能精確考慮波浪的風生機制又能反映出近岸復雜地形和建筑物的影響。 本文首先從流體力學理論出發(fā)回顧了風生波浪問題的由來，闡述風生波浪數(shù)值模擬的兩大難題（風生機制和傳播變形）及其各自數(shù)學模型的發(fā)展，尤其是CFD的出現(xiàn)給問題的求解帶來了便利條件。通過分析各個波浪數(shù)值模擬模型的優(yōu)缺點，第二部分給出了緩坡方程和SWAN模型的詳細說明。Berkhoff緩坡方程為一橢圓型方程，能夠刻畫波浪聯(lián)合折射、繞射、反射作用，經(jīng)過擴展已能夠考慮更多的動力機制，經(jīng)過改進發(fā)展出拋物型緩坡方程與雙曲型形緩坡方程�；趧幼V平衡方程的SWAN模型，以源匯項線性疊加的方式來考慮各種物理機制，對風生機制處理上比較精確。本文第三部分在考慮流作用的緩坡方程基礎上，建立了一個擴展的雙曲型緩坡方程，給出了具體的邊界條件，提出了ADI格式與C-N格式相結合的數(shù)值求解方法。針對輻射邊界條件中波向不確定問題，給出了沿空間推進的麥考馬克（MacCorMack）預估-校正的方法來求解波數(shù)矢無旋方程，從而得到計算域內(nèi)波向。第四部分選用了四個典型試驗地形對該擴展方程的適用性進行了驗證，給出了原雙曲型方程、擴展方程的計算結果與試驗值之間的對比，證明了本擴展模型的有效性。對于風生波浪的數(shù)值模擬，第五部分我們給出了一個SWAN自嵌套和擴展雙曲型緩坡方程聯(lián)合使用的方案，綜合利用了SWAN在刻畫風生機制和波-波作用上的合理性和擴展模型在描述波浪傳播變形方面的固有優(yōu)勢。
[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.
【學位授予單位】：杭州電子科技大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：P731.22

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