- 學位論文
平滑粒子流體動力學法在潰壩明渠流及潰壩引致洪水之數值研究
Numerical Investigation of Shallow-Water Dam Break Flows in Open Channels and Dambreak-Induced Flood Using Smoothed Particle Hydrodynamics
摘要
本研究應用平滑粒子流體動力學法(Smoothed Particle Hydrodynamics, SPH)之無網格數值模型，探討一維度潰壩明渠流和二維度潰壩引致的洪水淹沒等問題。SPH以拉格朗日(Lagrangian)觀點設計的薄片狀流體粒子(Slice Water Particles, SWP)和圓柱狀流體粒子(Cylindrical Water Particles, CWP)分別應用在一維度和二維度的SPH模式，用以研究潰壩明渠流及其引致洪水之分析。 本研究首先透過一維度乾濕床交界明渠河道及二維度潰壩流過乾床且平坦的洪水平原作為案例，進行SPH使用適當的粒子數之敏感度分析。爾後，延伸進行一維度及二維度SPH模式之驗證案例，包括了一維度的潰壩流通過一個粗糙且水平坡度的渠道、不同下游邊界條件設置的的渠道、和非定型渠道，及二維度的的潰壩流經過下游45度彎道、一間建築物座立於洪水平原的流場分析、義大利Toce河谷之縮尺模型試驗、和法國Reyran河谷及其下游洪水平原之縮尺模型試驗，進行實驗量測和現地試驗數據與數值模擬結果之交互比對。 SPH數值模擬結果說明了此法可精確地預測到衝擊間斷、激波運動、水躍、乾濕床移動邊界、超臨界/亞臨界/跨流、反流、收縮流、漫頂流、部分反射流和多波交互作用等流況。SPH數值模式在處理自由表面的不連續性、乾濕床移動邊界、及複雜地形變化有其優勢存在。透過上述多個研究案例之數值結果與實驗量測(或現地試驗)數據驗證，證明了SPH應用於一維度潰壩明渠流及二維度洪水淹沒問題的效率和可靠性。
並列摘要
A meshless numerical model is proposed to investigate shallow-water dam break flows in 1D open channels and 2D dambreak-induced flood and inundation. The numerical model is to solve the shallow water equations (SWE) based on smoothed particle hydrodynamics (SPH). The Lagrangian concepts of slice water particles (SWP) and cylindrical water particles (CWP) are adopted in the 1D SPH-SWE and 2D SPH-SWE formulations to generate horizontal flows and water surface variations in rivers and floodplains. The numerical sensitivity analysis is first performed to study the appropriate SWP/CWP number through dam break flows in an idealized 1D channel with dry-wet beds/through dam break flows in a dry flat floodplain. Extensive 1D validation by comparison with laboratory and field data is next conducted for four benchmark problems, including dam break flows through a rough flat channel, a rough bumpy channel with various downstream boundary conditions, and a nonprismatic channel. Then five numerical validations are next described to demonstrate the benefits and limits of the 2D-SPH-SWE modeling, including laboratory dam break flows through a dry 45°bend channel, a flat floodplain with an isolated building, and field dam break flows over the scale models of the Toce river valley in Italy and the Reyran river floodplain in France. The simulated results indicate that accurate performance is reached in the presence of shock discontinuities, shock front motion, hydraulic jumps, dry/wet bed flow, supercritical/subcritical/transcritical flow, reverse flow, contraction flow, overtopping flow, partial reflections and multiple wave interaction. A special attention is focused on the numerical performance of dealing with free-surface discontinuities, wetting and drying moving boundaries, and complex topography variations in rivers and floodplains. Thus, the proposed SPH approach has proved its efficiency and reliability for dam break flow computations in open channels and 2D flood and inundation problems.
參考文獻
延伸閱讀
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