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題 名 | 以等位函數法模擬自由渦流流場=Numerical Simulation of Free Vortex Flows by Level Set Method |
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作 者 | 廖清標; 陳政欣; 曹俊傑; | 書刊名 | 航空太空及民航學刊. 系列B |
卷 期 | 38:2 民95.10 |
頁 次 | 頁121-128 |
分類號 | 440.137 |
關鍵詞 | 等位函數法; WENO法; Runge-Kutta法; 渦流; Level set method; WENO scheme; Runge-Kutta scheme; Vortex; |
語 文 | 中文(Chinese) |
中文摘要 | 以等位函數來捕捉空氣與水交界面,使得複雜液面變化之流場能很有效率的計算出來。本文利用等位函數法和不可壓縮性Navier-Stokes方程式模擬三維自由液面流場。爲了確保等位函數爲到界面之距離函數,必須在每一時階加入重距離步驟,並爲了保證質量守恆,也加入了質量守恆限制式。在求解等位函數方程式,空間項採用了WENO法,時間項採用三階Runge-Kutta法。爲求解不可壓縮Navier-Stokes方程式,利用投影法導出壓力的Poisson方程式,再用二階顯示Adams-Bashforth法來解出下一時刻的速度場。本文以Zalesak問題來驗證對等位函數方程式的處理,結果顯示其正確性。在案例應用方面,本文進行三維自由渦流問題之數值計算,藉由是否有人工擾動觀察不同案例是否會產生渦流現象。 |
英文摘要 | This paper uses a level set function to capture the interface between air and water. The three-dimensional incompressible Navier-Stokes equations are used to solve the gas-liquid two phase flow system. In order to maintain the level set function as a smooth signed distance function from the interface, a reinitialization operation is required. We also apply a constraint to improve the conservation of mass significantly. A WENO scheme for space derivatives and third-order Runge-Kutta scheme for the time discretization are used to solve the level set equation. The projection method are used to derive a pressure Poisson equation to ensure the satisfaction of continuity equation. The velocity field can be obtained by second-order explicit Adams-Bashforth scheme, while the pressure is solved. The model allows us to simulate a wide range of flow regimes and surface tension effect can be consideration. We use the Zalesak's problem to test the accuracy of the model. This study applied to simulate three-dimensional free vortex flow problem. By adding if or not artificial perturbation to observe producing the vortex in different cases. |
本系統中英文摘要資訊取自各篇刊載內容。