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Solving a PDE in a volume (3D) coupled with a PDE on it's surface (2D)

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I am trying to model a two coupled PDEs using axisymmetric spherical geometry.

Here is a picture of the full 3D model:
imgur.com/nHTxMDh

Here is the axisymmetric reduction which you will see implemented in the COMSOL file later:
imgur.com/jWKwcj7

Here are the equations I am solving:
imgur.com/RGovKnu

We have two dependant variables, u_vit and u_ret, u_vit is defined within the sphere, u_ret is only defined on the surface Omega_1. Note, d may comfortably be set to zero, so that there exists no diffusion in theta.
Here s is non dimensional radius, therefore du/ds = \vec{n}\cdot\nabla u (give or take a minus sign).

I am attempting to formulate this using the weak form PDE. However I do not know how to implement the governing equation for u_ret. Would anyone be able to explain how this could be done? Or if this is not possible using the weak form PDE model is it possible with a different physics mode?

For reference, here is the weak formulation for u_vit, which is straightforward enough.
imgur.com/iGgWe4i

I have attached the comsol file, I have tried to label everything as obviously as possible.
www.dropbox.com/s/d85g1at2oc3c2cq/model_PI.mph?dl=0
(would attach using the 'attach file' button, had to use a Dropbox link)

0 Replies Last Post Nov 23, 2016, 10:23 a.m. EST
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