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標題: | 與彈性底床及不規則介面耦合之三維海洋音傳模擬 Modeling 3D Wave Propagation in the Ocean Coupled with Elastic Bottom and Irregular Interface |
作者: | Li-Wen Hsieh 謝力文 |
指導教授: | 陳琪芳(Chi-Fang Chen) |
關鍵字: | 拋物線聲波方程式,三維音傳,不規則流體/彈性體介面,流體/彈性體耦合波,C4PM,隱式有限差分方法,剪力效應, Parabolic wave equation,3D sound propagation,Irregular fluid/solid interface,Fluid/solid coupled wave,C4PM,Implicit finite difference method,Shear effect, |
出版年 : | 2005 |
學位: | 博士 |
摘要: | 本文目標在於透過求解拋物線聲波方程式,以模擬聲波在三維海洋環境中與彈性底床以及不規則介面耦合之傳播現象。過去為了簡化問題,常將底床的彈性特質忽略而視同流體,因此並未將剪力波的效應考慮在內;然而過去主要在深海環境中因為聲波與底床之接觸有限尚且容許如此的簡化,一旦環境改為淺海時,聲波能量進出底床的比例增加,剪力波的影響便不容忽視。因此底床之彈性特質必須被考慮在內,俾使聲波之傳播能夠被正確地呈現。就數值計算上而言,過去由於硬體資源有限,而捨真實的三維環境,改採經由軸對稱之假設簡化而成的二維環境;然而若要符合實際海洋環境空間上之變化,尤其在淺海環境中地形水文等參數隨空間變化程度甚大,軸對稱之假設無法成立,必須採三維之考量;加以電腦軟硬體之發展日趨進步,過去計算資源上的限制亦逐漸放寬。在此發展下,本論文將提出一個改進的數學模式用於預測在一個三維海洋環境中與不規則流體/彈性體介面耦合的聲音傳播,並提供一個隱式有限差分方法以獲得此一數學模式的數值解,用以建立一個計算模型C4PM。對於該模型採用的拋物線方程式解法程序步驟,本文從理論以及數值計算兩個角度加以討論。隨之將包含數個算例,透過與目前已知的參考解作比較,以顯示該計算模型的確有能力處理具有剪力效應的問題,並且能夠得到一符合預期的數值解。最後並提出接續本研究之未來期望發展方向與工作項目,包含數項可精進模式的方法,如採用廣角方法、重新衡量遠場近似之應用、起始聲場之計算、探討更一般化之三維流體/彈性體介面以及拋物線方程式模型之能量守恆性質等。 This dissertation is focused on modeling 3D wave propagation in the ocean coupled with elastic bottom and irregular interface by solving parabolic wave equations. In the past few decades the elastic properties of ocean bottom were usually ignored to simplify problems by assuming a fluid seabed. Nevertheless, while it is acceptable to make such assumptions in deep water, the effects of shear waves can never be omitted as long as sound waves penetrates into ocean bottom, especially in shallow water where interactions between sound waves and elastic bottom are very frequent. Hence, seabed has to be considered as elastic solids to correctly reveal the propagating behavior of sound waves. Besides, due to the shortness in hardware resources in the past, real 3D problems were often simplified to 2D through axial symmetry assumptions; however a real 3D environment must be taken into consideration especially in shallow water where the assumptions may not valid. In addition, the development of hardware and software is in huge progress so that limitation on computational resources has been gradually released. Under such circumstance, a novel mathematical model and an implicit finite difference method to obtain a numerical solution for predicting wave propagation in a 3D ocean coupled with irregular fluid/solid interface are presented and developed into a computer code C4PM in this dissertation. Theoretical and computational aspects of the proposed parabolic equation solution procedure are investigated. Several numerical examples are included to show satisfactory results after comparing to known reference solutions with shear effects. Finally the directions of future works are proposed which may enhance the model including the application of wide-angle scheme, revaluation of far-field approximation, generation of initial field, generalization to a 3D interface, and energy conserving property of PE model. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34927 |
全文授權: | 有償授權 |
顯示於系所單位: | 工程科學及海洋工程學系 |
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