變質量平滑粒子動力法在降雨逕流系統之模擬

Modeling rainfall-runoff processes using smoothed particle hydrodynamics with mass-varied particles

張佑聖(Yu-Sheng Chang)

指導教授 ： 張倉榮

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/博士(2017年)

https://doi.org/10.6342/NTU201700904

摘要

平滑粒子動力法(Smoothed Particle Hydrodynamics, SPH)為一種拉格朗日(Lagrange)觀點下的無網格粒子數值模擬方法。相較於傳統固定式網格數值方法，SPH在處理自由液面與大形變流場問題上已被許多研究證實具有優勢。近期SPH被運用在求解淺水波方程式(shallow water equations, SWEs)去模擬或是處理各種水力學問題，而發展出SPH-SWEs模式。然而，由於SWEs維度上的限制，目前SPH-SWEs無法處理計算維度外流體增減的問題，如側流、降雨和入滲等現象。因此本研究發展變質量平滑粒子動力法，藉由流體粒子資量的增加或減少來模擬額外維度上流體的增減，並將此新模式運用於研究降雨逕流過程中相關之問題上。
為了測試此新發展之變質量SPH法，研究中選取了三個具有代表性的案例進行模擬。模擬案例包含一維平坦傾斜渠道上的均勻降雨、一維三坡度渠道上不同降雨延時之非均勻降雨與二維複雜地形上之均勻降雨。模擬結果顯示本研究所發展之模式可以不使用源項函數以及增加粒子數來處理增加的流體質量，且在降雨經流過程中所出現的水躍、乾溼床移動邊界流及超臨界/亞臨界/跨流等現象上，皆有不錯的吻合程度，因而證明了此變質量SPH法的穩健與可靠性。
本研究中亦將此變質量SPH法在運用於處理入滲的問題上，結合霍頓(Horton)入滲方程進行求解，模擬逕流時流體減少之現象。另外，本研究亦嘗試以兩分量壓力近似法(Two-component Pressure Approach, TPA)建立一維SPH下水道模式。藉由TPA可使得SPH能以單一控制方程式來同時模擬滿管壓力流與自由夜面流的流況。而透過變質量流體粒子的運用，可將降雨逕流模式(增質量)、入滲模式(減質量)與下水道模式(質量傳輸)結合成一套SPH淹水模式。

關鍵字

平滑粒子動力法 ； 淺水波方程式 ； 無網格方法 ； 變質量粒子 ； 降雨逕流過程 ； 入滲 ； 下水道

並列摘要

Smoothed Particle Hydrodynamics (SPH) is a kind of meshless particle numerical method with Lagrangian concept. Compared to traditional grid-based method, SPH is proved by many researches that it has advantages on dealing with free surface and large deformation problems. Recently SPH has been implemented on solving shallow water equations (SWEs) for simulating or handling the hydrodynamic problems and SPH-SWEs has been developed accordingly. However, due to the limitation of dimensions of SWEs, SPH-SWEs still cannot process the problems of fluid inflow /outflow beyond the computational domain, e.g. lateral flow, rainfall, and infiltration, etc. Thus this research constructs the mass-varied SPH model which uses the mass variation of fluid particle to simulate the fluid inflow/outflow on the external dimension and also applies this new model on investigating the rainfall-runoff processes.
To validate this novel mass-varied SPH model, three benchmark case studies are adopted to conduct numerical simulations, including uniform rainfall over a 1D flat sloping channel, nonuniform rain falling over a 1D three-slope channel with different rainfall durations, and uniform rainfall over a 2D plot with complex topography. The simulated results indicate that the proposed treatment can avoid the necessity of a source term function of mass variation, and no additional particles are needed for the increase of mass. Rainfall-runoff processes can be well captured in the presence of hydraulic jumps, dry/wet bed flows, and supercritical/subcritical/transcritical flows. The proposed treatment using mass-varied particles was proven robust and reliable for modeling rainfall-runoff processes.
In this thesis the mass-varied SPH model is also utilized on solving the infiltration problems associated with Horton formula to simulate the fluid decrease during the runoff process. In addition, this research tries to develop a one-dimensional SPH sewer model with two-component pressure approach (TPA). With this approach, SPH can simulate the full-pipe pressure flows and free surface flows at the same time with single governing equation. Afterwards in future study, by means of mass-varied fluid particles, we can integrate the rainfall-runoff model (mass addition), infiltration model (mass reduction) and sewer model (mass transfer) into a SPH flood model.

並列關鍵字

Smoothed particle hydrodynamics ； Shallow water equations ； Meshless method ； mass-varied particle ； Rainfall-runoff process ； Infiltration ； Sewer

參考文獻

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