Boundary Element Solutions of Two-Dimensional Steady Stokes Flows Based on Primitive Variable Formulation

使用原始變數表示式之二維恆態史托克流場邊界元素解法

黃立政(Li-Jeng Huang)

《中國航空太空學會學刊》 30卷4期 (1998/12) Pp. 261-268

https://doi.org/10.6124/TAASRC.199812_30(4).02

摘要

本研究旨在發展一個基於原始變數表示式之邊界元素解法用以分析二維恆態史托克流場。由勞倫茲反位定理可推導出包含邊界速度與邊界曳引力之速度分量積分方程式，離散化邊界後得到線性聯立方程式其中所有場量均爲邊界速度及曳引力。一旦求出全部之邊界速度及曳引力，內部點之速度、壓力、渦量、剪應力等均可表成邊界積分之型式計算。將邊界元素法應用於兩平行板間擠壓黏滯性流場及壁動引發穴流之流場分析，探討其收斂性與正確性，並與解析解或有限元素法比較，結果相當理想。

關鍵字

不可壓縮黏住流場 ； 恆態史托克流場 ； 邊界元素法 ； 原始變數表示式

並列摘要

In this paper a boundary element method based on primitive variable formulation for two-dimensional steady Stokes flow is presented. By the use of Lorentz, reciprocal theorem for steady incompressible viscous flow the boundary integral equations for the velocity field are derived. Discretization of boundary of the problem leads to a system of equations wherein all the unknown velocity and traction components are on the boundary nodes. Once these boundary velocities and tractions are calculated, the velocities, pressure, shearing stresses and vorticity at each internal point can be obtained from the boundary integral representations along with various kernel functions. Two examples including flow squeezed between two parallel plates as well as wall driven cavity flow are employed to test the algorithms. It is found that excellent agreement is obtained between the boundary element results and the available analytical and finite element results.

並列關鍵字

incompressible viscous flow ； steady Stokes flow ； boundary element method ； primitive variable formulation