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How combine 2D PDE with 1D ODE for boundary
Posted May 19, 2011, 9:37 a.m. EDT 0 Replies
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How can I add boundary condition (constraint) for 2D model as a solution of 1D ODE defined on this boundary? I use PDE interface.
The physical problem is:
Two electrodes (high voltage and grounded, the grounded one is covered with dielectric film). Dependent variable is 'u' - electric potential. Laplace equation for u in two domains (dielectric and free space). Dielectric surface charged due to electric field:
dsigm/dt ~ n*grad(u), sigm = surface charge defined on 1D boundary.
Initial condition: sigm = 0.
I have to determine ODE for sigm in separate 1D model (mod2) because of Comsol can't combine 2D and 1D equations in the same model (is this correct?).
This surface charge affect on boundary condition for Laplace equation (mod1). Constraint for dielectric surface is:
nx*up(ux) + ny*up(uy) - epsilon* (nx*down(ux) + ny*down(uy) ) + mod2.sigm/epsilon0_const *1[F/m]
I have tried to couple 2D and 1D models with Identity Mapping
... +mod2.idmap2(mod2.sigm/epsilon0_const *1[F/m] )
but get "Wrong map search dimension in extrusion coupling operator."
Can you help ?
Hello Vladimir Karalnik
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