Green's theorem or divergence theorem?
I want to calculate the total flux but I'm not sure if I have to use Green's theorem (2D) or the divergence theorem (3D). The equation below is a modified Reynolds equation describing the air flow in the clearance of porous air bearing.
P is the pressure in the clearance of the air bearing, P' is the pressure in the porous media. However, at Z=1 P' must be equal to P for continuity.
This equation can be rewritten using the divergence vector operation:
Solving this equation with a numerical method (i.e. finite difference) can be done by first simplifying the equation with Green's theorem for flux or the divergence theorem. Because I'm interested in the flow in the - Y direction I want to solve the equation applying Green's theorem (2D). However, in the first equation there is also a gradient in the Z-direction namely . So my question is: Can I calculate the flux with Green's theorem or do I have to use the divergence theorem because of the pressure gradient in the Z-direction?
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