- 學位論文
以平滑粒子動力法研析淺水波汙染物傳輸問題
Numerical Investigation of Shallow-Water Pollutant Transport Problems with Smoothed Particle Hydrodynamics Method
摘要
本研究主要在運用平滑粒子動力法(Smoothed Particle Hydrodynamics, SPH)求解淺水波中的汙染物傳輸問題。SPH為一種拉格朗日(Lagrange)觀點下的無網格粒子數值模擬方法。在拉格朗日觀點下，流體控制方程式不需要離散非線性對流項。所以SPH法可以輕易地處理大形變問題、自由液面、乾濕床問題以及超亞臨界流況混合的問題。因此，SPH非常適合用來求解對流-擴散方程式，並用以研究地表上各種流況中的汙染物傳輸問題。 研究中首先以Top hat tracer分佈和初始脈衝函數為基準案例，展現出此模型相較於以往模型的優勢之處，並使用不同的粒子數進行敏感度分析。本研究中所建立的汙染物傳輸模型不但能夠處理任意Peclet數的下的流況，而且此模型和傳統網格法比較下，幾乎沒有數值擴散和數值震盪的現象產生，模擬的結果亦相當地準確。爾後，使用流經一凸塊的流場來測試此模型在開放式邊界條件和不規則地形的條件下求解對流-擴散方程式的能力。接著，使用黎曼問題(Riemann problems)中的潰壩問題來檢驗模型，即便在流場中產生在震波或是稀釋波，使得流場出現不連續面的情況下，此模型仍舊可以相當精確地解出汙染物分佈的濃度場。最後，則是以二維的淺水波流場—二維均勻流來驗證當以對流為主的傳輸過程和以擴散為主的傳輸過程中，發生在主流方向和側流方向時汙染物濃度場的分佈狀況。本文就以上各個研究案例的數值結果與比較探討，研析在SPH架構下所建立的汙染物傳輸模型之效率及可適性。
並列摘要
In this research, Smoothed Particle Hydrodynamics (SPH) is applied to solve the transport of pollutant problems shallow water flow. SPH method is a meshfree numerical method under the Lagrangain viewpoint. Under this viewpoint, the non-linear advective terms of the fluid governing equations does not need to be discretized. Furthermore, SPH method can easily deal with the large deformation problems such as free surface, dry-wet interface and the super/subcritical mixed flow problems. Hence, this is why it is very suitable to be introduced in this work to investigate the pollutant transport problems in arbitrary flow conditions on the ground. First, the benchmark tests, like the top hat tracer distribution and impulse point release, are used to demonstrate the advantages of this pollutant transport model compared to the results of previous studies, and then the numerical sensitivity is performed with different particle numbers. The pollutant transport model set up in this research not only can handle the flow conditions of entire range of Peclet numbers from zero to infinity, but also produces few numerical dispersion and numerical oscillations when compared with traditional grid methods. In addition, the simulations always have the reasonably accurate results. Afterwards, the flow over a bump is used test the abilities of this model on solving the advection-diffusion equation under the open boundary conditions and the irregular terrain conditions. Next, one kind of the Riemann problems, i.e. the dam break problems, is carried out to examine that the pollutant transport model is able to obtain the concentration distribution of the pollutant precisely, even encountering shocks or rarefaction waves in the flow field. The final part focuses on the two dimensional shallow water flow–the two dimensional uniform. The concentration field of the pollutant distribution is observed when the advective transport process and the diffusive transport process are occurred in mainstream direction or in lateral direction. In general, the pollutant transport model established under the SPH frame has proved its efficiency and reliability by above numerical results and case comparisons.
參考文獻
延伸閱讀
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