# Lid-driven Cavity in 2D

## Problem Description

A square cavity with a side length of L°= 1e^{-3°} m is filled with water
(density: 1000 kg/m^{3}, dynamic viscosity: 1e^{-3} kg/m/s). The
upper wall is moved with a constant velocity U_{0} imposing a rotational
movement of the fluid in the cavity. Here, the configurations with Re°=°100,
Re°=°1000 and Re°=°10000 are simulated by adjusting the velocity of the lid
correspondingly. The highly-resolved Finite-Difference calculations by Ghia et al.
^{2} with a grid resolution of 257x257 are taken as reference.

## Numerical Setup

## Results

^{2}at finer resolutions of 100x100 and 200x200, respectively. This is expected as higher Reynolds numbers results in finer structures and requires more particles to resolve.

^{1}S. Adami, H. Hu and N. Adams, "A generalized wall boundary condition for smoothed particle hydrodynamics,"

*Journal of Computational Physics,*vol. 231, pp. 7057-7075, 2012.

^{2}U. Ghia and K. S. C. Ghia, "High-Re solutions for incompressible flow using the Naview-Stokes equations and a multigrid method,"

*Journal of Computational Physics,*vol. 48, pp. 387-411, 1982.