方腔驱动流的数值解

方腔驱动流的数值解

数值解 lid-driven cavity flow¹²³⁴⁵

• 考虑雷诺数 \(Re=1000,5000,7500\),

• 二维问题，\(Re\approx7500\) ，会出现出现 Hopf bifurcation⁶,

• \(Re<7500\), 收敛到稳定解,

• \(Re>7500\), 稳定解和周期解。如果稳定解存在，初解和空间分辨率选取适当，那么能得到稳定解。

结果比较:

1. 图流线图
2. 画出 \(x =0.5\), \(y =0.5\) 两条线上，u, v, p，

---

1. Griffith, Boyce E. 《An Accurate and Efficient Method for the Incompressible Navier–Stokes Equations Using the Projection Method as a Preconditioner》. Journal of Computational Physics 228, 期 20 (2009年11月): 7565–95. https://doi.org/10.1016/j.jcp.2009.07.001.↩︎

2. U. Ghia, K.N. Ghia, C.T. Shin, High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method, J. Comput. Phys. 48 (3) (1982) 387–411.↩︎

3. O. Botella, R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluid 27 (4) (1998) 421–433.↩︎

4. E. Erturk, T.C. Corke, C. Gökçöl, Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, Int. J. Numer. Methods Fluid 48 (7) (2005) 747–774.↩︎

5. C.J. Roy, A.J. Sinclair, On the generation of exact solutions for evaluating numerical schemes and estimating discretization error, J. Comput. Phys. 228 (5) (2009) 1790–1802.↩︎

6. Y.-F. Peng, Y.H. Shiau, R.R. Hwang, Transition in a 2-D lid-driven cavity flow, Comput. Fluid 32 (3) (2003) 337–352.↩︎