- 學位論文
混合式有限體積動力波地表漫地流模式之研發與應用
A Hybrid Shallow Water Solver for Overland Flow Modelling in Rural and Urban Areas
摘要
本研究旨在發展準確且快速的有限體積動力波地表漫地流模式，來針對鄉村與都市地區的漫地流進行模擬。此模式建立了一個新的混合方法，來先根據水位不連續程度的大小來將模擬域中流況進行分類，並且在較為平緩的流況下此模式採用了Rusanov方法來計算有限體積法所需的通量，而在強烈不連續流況下則採用HLLC方法來計算。由於兩個通量計算方法在數值上存在差異，為了避免在模擬域中過於劇烈的切換兩個通量計算方法而導致數值上的不平衡，因此混合方法會再導入兩個通量計算方法都使用的區域來減緩此情形。三個有解析解且流況有強烈不連續流的案例被選定來進行此模式的模式檢定，隨後此模式再通過三個分別代表鄉村、都市地區不同流況的案例來進行驗證。所選定的三個案例分別為建物周邊的降雨–逕流模擬、潰壩洪水衝擊下游建築物群模擬與街道交叉口水流模擬等。除了比較與單純使用前兩個通量計算方法於準確性上的差異之外，此模式在演算效率上的改進亦被仔細地評估來說明此模式的貢獻。在以上案例內，比較的重點在於局部模擬區域中此模式對於強烈不連續流的準確性，以及於整體模擬區域的演算效率。結果顯示，本研究所發展的混合式有限體積動力波地表漫地流模式可達到如單純使用HLLC方法一樣的準確度，但卻能省下大量的計算時間。另外，此模式的演算效率與所牽涉到的流況有關，當模擬域中有劇烈變化的流況愈少，此模式的演算效率可以更高。在證明此模式可以準確且有效率的進行包含劇烈變化流況的漫地流模擬後，此模式還可以與能加快演算效率的方法如局部時間步長(local time stepping)、平行化(parallelization)等方法進行組合來加強此模式的演算效率。另外，除了本研究所採用的兩個數值通量計算方法之外，其他數值通量方法亦可以被本研究所提出的模式使用，來根據所欲求解的問題來搭配組合為新的漫地流模式。由此，本研究所發展的模式具有相當大的潛力來運用於淹水模擬上。
並列摘要
This study aims to present an accurate and efficient finite-volume approach for overland flow modelling in rural and urban areas through solving the two-dimensional shallow water equations. The proposed approach introduces a hybrid procedure that utilizes the sharpness of discontinuity to identify flow conditions in the entire computational domain, and then a low-accuracy/high-efficiency scheme (the Rusanov scheme) is used in regular flows, whereas a high-accuracy/low-efficiency scheme (the HLLC scheme) is adopted in strong discontinuous flows. Regions that simultaneously adopt the two schemes are artificially specified to diminish numerical unbalances between the two schemes. Model calibration is carried out through three strong discontinuous flow cases with the exact solutions. Model verification is next described by three benchmark cases, including rainfall-runoff around buildings, flash floods towards buildings, and street junction flows. Model efficiency assessment is also conducted to present the numerical efficiency improvement of the proposed approach for various flow conditions. Technical attention is devoted to the numerical performances on local accuracy and global efficiency of the proposed approach. The simulated results indicate that the proposed approach can simulate as accurate as the HLLC scheme with significant reduction on its computational time. How efficient the proposed hybrid approach can reach depends on flow conditions involved. It is more efficient than the HLLC scheme as the portion of strong discontinuous flows in the computational domain is relatively smaller. The proposed approach has proved its accuracy and efficiency for overland flow modeling, and it can also be used together with other speed-up techniques, such as local time stepping and parallelization, to improve its efficiency. Other finite volume schemes can also be utilized to improve the efficiency and accuracy of the proposed approach. Therefore, the solver has considerable potentials as a useful tool in flood inundation simulations.
參考文獻
延伸閱讀
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