質點法應用於河川汙染物傳輸之模擬

本研究應用Lagrangian質點法解質量傳輸方程式，進行河川中污染物二維傳輸的數值模擬。質點隨著水流的運動，濃度的擴散受濃度之傳輸方程式控制。在Lagrangian的觀點下，質點隨著水流的移動，而濃度因擴散或延散(dispersion)現象而改變。使用Lagrangian質點法具有無網格的特性，且質點只存在於有濃度之處，可以集中計算資源在濃度場的模擬，並且可以提升計算的精準度。首先以質量傳輸方程式為控制方程式，為了能充分發揮質點法的優勢，擴散或延散現象以質點強度交換(Particle Strength Exchange, PSE)法處理。使用質點強度交換法(PSE)處理Laplacian項時，每個時步須對計算質點做從新分配 (redistribution) 的動作，使濃度質點能均勻分配置均勻格點上，以維持PSE法之收斂。為了降低計算的困難度，將延散係數設定為定值。模式建立後，將以典型的二維濃度擴散問題進行驗證。例如在一流向單一且流速均勻的無限寬廣河道及有邊界影響下之河道，瞬間注入一點源或持續添加濃度於河道中，觀察其擴散情況，並進行驗證。此外，將模擬在一矩形感潮河口，在得知河口潮波條件後，以多種河口條件下，例如河道在斷面方向的地形、注入連續汙染源的時間，探討其質量傳輸在感潮河口段的擴散情況並進行分析。

關鍵字

質點法；質點強度交換法；擴散；質量傳輸

並列摘要

This study develops a numerical model to simulate two-dimensional mixing in rivers and estuaries using a Lagrangian particle method. In this model, concentration is discretized by a series of particles. Using a Lagrangian frame, the positions of particles shift along the fluid flow, and their strength updates due to diffusion and dispersion. The major advantage of this model is the essentially grid-nature of the particle method, which may reduce the numerical dissipation in solving the mass transport equation, and also concentrate the computational resources on the simulation of concentration field which is predominantly confined in a compact region. To accomplish the simulation of mass transport in Lagrangian frame, the rate of change of particle strength is calculated using a Particle Strength Exchange (PSE) scheme. At each time step the redistribution of particles is performed to interpolate the concentration onto a mesh to maintain the overlapping of particles for the stability criterion of PSE. To reduce the difficulty of compution, in all simulations the dispersion coefficient is set to be a constant. Severl benchmark problems of two-dimensional advection-diffusion equation were simulated using this mode fo validation, such as the impulsive injection of point source in the uniform flow in an infinite-wide channel and a channel with boundaries, and the spread of a plume from a point source. The comparisons between numerical and analytical results show good agreements. To test the capability of the model, the mixing of contaminant in a rectangular estuary with simplified geometry caused by a monotonic tidal wave was simulated, and the longitudinal dispersion in the estuary due to the shear flow caused by the variation of bed geometry was investigated.

並列關鍵字

Mass transport ； Particle strength exchange ； Particle method ； Diffusion

參考文獻

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質點法應用於河川汙染物傳輸之模擬

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