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Lid driven cavity in 2D with multilevel

Lid-driven cavity is a simple 2D problem with simple boundary conditions. In a square domain, dirichlet boundary conditions are set on all sides. Fixed wall ($\vec{u} = 0$) boundary conditions on 3 sides (west, east and south) and moving wall ($u_x = u_c, u_y = 0$) boundary condition on north side.