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Solving 2D Poisson Equation in 3D geometry

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Old   November 20, 2015, 20:08
Default Solving 2D Poisson Equation in 3D geometry
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Ender Demirel
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Hi foamers,
I have a three dimensional geometry and I'm trying to solve Poisson equation. I can solve the three-dimensional Poisson equation --> d2(psi)/dx2+d2(psi)/dy2+d2(psi)/dz2=S_psi using the following code:
solve ( fvm::laplacian(gamma, psi) == S_psi );

But I would like to solve the Poisson equation at only xy planes of the geometry excluding the derivative in z direction. Finally, my modified equation will be d2(psi)/dx2+d2(psi)/dy2=S_psi,

here psi is my dependent variable and is the function of x, y and z.

How can I solve that two dimensional Poisson equation in the internalfield of a three-dimensional geometry?

Thanks,
Ender
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