以速度－渦度列式法求解三維不可壓縮流場

Velocity-Vorticity Formulation for 3D Incompressible Flow

廖清標(C. B. Liao) ； 盧泰成(T. C. Lu) ； 吳銘順(M. S. Wu) ； 楊德良(D. L. Young)

《中國航空太空學會學刊》 32卷1期 (2000/03) Pp. 57-63

https://doi.org/10.6124/TAASRC.200003_32(1).06

摘要

本文利用速度－渦度列式法採用有限差分法來求解不可壓縮、粘性流體之運動，以三維穴流及三維後向階梯流流場爲例，分別進行數值計算工作。數值模式以顯示Adams-Bashforth法來求解Helmholtz vorticity transport equation；對速度之Poisson方程式則利用快速傅利葉轉換(FFT)法直接解出。配合MAC交錯網格系統，在求解過程不需要过度的邊界條件，且速度與渦度在求解過程中可以不必疊代程序，數值解的精確度不論在時間或空間上都具二階精確度。初步研究結果經與前人研究之實驗及數模比較，顯示本文數值模式相當成功。

關鍵字

速度－渦度列式法 ； 三維流 ； 穴流 ； 後向階梯流

並列摘要

The motion of incompressible and viscous fluid in a three-dimensional square cavity and three-dimensional backward-facing step are solved by the finite difference method using the velocity-vorticity formulation.
For the calculation of vorticity transport equation, explicit Adams Bashforth scheme is proposed. The Fast Fourier Transform (FFT) is suggested to directly solve the velocity Poisson's equation. In conjunction with staggered grid system, the boundary condition of vorticity is satisfied automatically and without any consideration.
Iteration process is not necessary in the solving process between velocity and voroticity of proposed numerical method. By the way, the numerical solution reaches second-order accuracy in both time and space. The preliminary results of this study show that the numerical method is quite successful.

並列關鍵字

velocity-vorticity formulation ； three-dimensional flows ； cavity flow ； backward-facing step flow