Cavity_FDM_NumPy

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FDM (Finite Difference Method) simulation of 2D lid-driven cavity flow based on :

fractional step method for time integration
Kawamura-Kuwahara scheme (3rd-order upwind -> 4th-order central with 4th-order numerical viscosity) for convection
2nd-order central difference for pressure gradient and viscosity terms

The results are compared with the reference solution (for velocity) presented in Ghia+1986.

Results

Cavity flow is a steady problem. We consider that the field has reached to a steady state when the following is satisfied:

$$\max \left( \frac{\| u^{(n+1)} - u^{(n)} \|_2}{\| u^{(n)} \|_2}, \frac{\| v^{(n+1)} - v^{(n)} \|_2}{\| v^{(n)} \|_2} \right) \le \delta$$

where $\delta$ is the convergence tolerance, set to $\delta = 10^{-6}$.

The following summarizes results at different Reynolds numbers and different resolutions.

Column name	Description
Re	Reynolds number (inertia vs viscosity)
t	Dimensionless time until the convergence (when velocity residual $\le \delta$ is met)
u	Horizontal velocity along the geometric center
v	Vertical velocity along the geometric center