Navier-Stokes Problem: Solving for Pressure Gradient in a 2D Rectangular Cavity

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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?

cosh cos, cosh sin, sinh cos, sinh sin

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##?
 
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##?
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.