The discussion focuses on solving the Navier-Stokes equations for a 2D rectangular cavity filled with liquid, where the top plate moves with velocity V_0. The participants derive the velocity profile and pressure gradient, concluding that the pressure gradient is significant and necessary for flow analysis. They emphasize the importance of boundary conditions and integral constraints in solving the equations, particularly in low Reynolds number scenarios. The conversation also touches on the use of stream functions to satisfy continuity equations and visualize flow patterns.
Fluid dynamics researchers, mechanical engineers, and students studying fluid mechanics who are interested in the mathematical modeling of flow in confined geometries.
Chestermiller said:I'm having second thoughts on your equation for ##\omega##. Shouldn't it be a function of x times a function of y, not the sum of such functions?
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No. Solve the equations involving both omega and psi. The only tricky part is numerically specifying the boundary conditions on omega. But I know how to do that.joshmccraney said:Shoot, you're totally right. Then ##\nabla \cdot \psi = \omega## is not separable. I can't think of a way to analytically solve. How would you do this numerically? Finite difference ##\nabla^4 \psi=0##?