無網格移動粒子半隱式法程式建立及應用

近年來在計算流體力學技術的發展上，一種新的數值方法即無網格法，得到了的關注。在目前學術研究領域已有十餘種無網格法。本文對其中一類無網格粒子法即移動粒子半隱式(MPS)法，進行研究。本文從無網格法建立近似函數時所採用的近似方法及對控制方程式所進行的等效變換出發，對現有的無網格法進行歸類，並提出無網格法在求解物理問題中所具有的優勢，同時也說明無網格法發展及其在工程應用中所存在的一些挑戰。在閱讀前人文獻的基礎上，根據移動粒子半隱式法的基本思想，對其建立了各種粒子的作用模型，進行了詳細的算法推導並編譯程式，以水柱崩塌、液滴衝擊水面及浮體在波浪中的橫搖角度進行了數值模擬計算，並對三個算例的結果進行了分析，驗證了移動粒子半隱式法在模擬流體自由液面中所具有的優勢。

關鍵字

MPS法；移動粒子半隱式法；無網格法；自由液面流；不可壓縮流

並列摘要

In recent development CFD algorithms and schemes, a strong interest is focused on a new numerical method: meshfree method. In this thesis, the moving particle semi-implicit (MPS) method, one of the meshfree particle methods, is studied with a depth. They are different in the means of function approximation and implementation process. Several typical meshfree methods were surveyed and classified. Both advantage and disadvantage of this kind of computational method were summarized. Based on the previous research, the particle interaction models and the algorithm of MPS method were developed. Three examples, collapse of liquid column, drop impact on the liquid surface and floating body rolling in waves were successively simulated. Analyses were also made, which shows MPS of special advantage in simulating fluid free surface flow.

並列關鍵字

MPS Method ； Moving Particle Semi-Implicit Method ； Mesh-Free Method ； Free Surface Flow ； Incompressible flow

參考文獻

[1] Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., Krysl, P.“Meshless methods: An overview and recent developments”, Comput. Methods Appl. Mech. Engrg., 139:3-47, 1996.

[2] Lucy, L.B.“A numerical approach to the testing of the fission hypothesis”, The Astron. J., 8(12):1013-1024, 1977.

[3] Monaghan, J.J.“An introduction to SPH”, Comput Phys. Comm., 48:89-96, 1988.

[4] Swegle, J.W., Hicks, D.L., Attaway, S.W.“Smoothed particle hydrodynamics stability analysis”, J. Comput. Phys., 116:123-134, 1995.

[5] Dyka, C.T.“Addressing tension instability in SPH methods”, Technical Report NRL/MR/6384, NRL, 1994.

國際替代計量

無網格移動粒子半隱式法程式建立及應用

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