新平滑粒子動力法對於明渠側入流流況之研析

Abstract

本研究以平滑粒子動力法 (smoothed particle hydrodynamics, SPH) 建立SPH側入流模組，並應用於明渠側入流問題之探討。SPH為一種拉格朗日 (Lagrangian) 觀點描述流體運動的無網格數值方法，由於SPH是以粒子呈現物理空間，且粒子會隨時間變化移動位置，相較傳統網格法，SPH在如何描述固定位置的側入流影響主流流況上是較不易執行。 在SPH中的粒子本身帶有質量，本研究試圖利用權重方式將側入流流量增加至側入流處鄰近粒子的質量上，以計算粒子的水位變化，並在動量方程式考慮側入流流量給予的動量變化。此外，因應模擬過程粒子質量變化，修正傳統平滑長度在每個時間間距的更新公式，建立以粒子體積為參數的平滑長度更新公式。本研究利用三個研究案例來測試新SPH模式在側入流流況預測上之能力，包括穩態單點側入流系統、非穩態單點側入流系統與非穩態多點側入流系統。將模擬結果與HEC-RAS模式進行比較，發現兩者在結果上有一致性，此說明本研究所發展的新SPH模式具有準確性與應用性。

In this research, smoothed particle hydrodynamics (SPH) is applied to solve shallow water equations and investigate the lateral flows in open-channels. SPH is a meshfree numerical method based on the Lagrangian viewpoint to describe the motion of fluid. Particles are used to discretize spatially the computational domain in SPH. Since particles move freely with time in SPH, the effect of lateral flows on main channels estimated by SPH is more difficult than mesh-based numerical methods. In SPH, each particle has its own mass. The approach of increasing each particle mass by a weighting summation is proposed to update the water depth of each particle at every time step. In addition, the evolution of a smoothing length of each particle depends on the volume instead of the density herein. In this research, three study cases, including steady flows in single lateral-channel systems, unsteady flows in single lateral channel systems and unsteady flows in multi-lateral channel systems, are used to test the ability of the new SPH model on the simulation of lateral flows in open-channels. To compare with a mesh-based numerical package called HEC-RAS, the SPH and the HEC-RAS simulated profiles of the discharge and the water depth are consistent. Thus, the new SPH is capable of handling lateral flows in open channels.