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Coefficient Form
Posted 2011年5月12日 GMT-4 16:41 Version 4.1, Version 4.2 3 Replies
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I am fairly new to COMSOL and am attempting to define a new PDE for an axisymmetric model. I'm am trying to use the coefficient form interface, but I'm getting very confused by the notation. The documentation indicates that the dependent variable is, by default a scalar. I would like to define my dependent variable as a vector (specifically, a velocity with components in the radial and axial directions).
As best as I can figure, the way to do this is to change the number of dependent variables to two. But if this turns the dependent variable into a vector, the dimensions of the other components of the PDE don't seem to add up. For instance, the diffusion coefficient becomes what appears to be a 2x2 array of 2x2 matrices, whereas the gradient of the dependent variable vector would itself be a 2x2 matrix. I also do not understand why the terms alpha, beta, and gamma are defined component-wise.
Any clarification on the use of this interface or its notation would be most welcome. Thanks.
David
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did you open your new PDE coefficient form as a 1D, 2D or 3D phyiscs model ?
that changes the way the variables are grouped and considered
--
Good luck
Ivar
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I am also really confused about this. I'm using a 2-D Cartesian model, with the Coefficient-form PDE model. Two dependent variables. Given that the right side of the equation is a 2-element vector 'f' (the source term), that means each term on the LHS must also be a two-element vector.
So, let's just look at the convection coefficient (beta), term: β · ∇u
Where u = 2-element vector (the two variables I'm solving for, namely Ex and Ey)
∇= 2-element pseudo-vector [d/dx, d/dy]
β = 8-element (!) rank-3 tensor??
I'm trying to implement two equations:
dEx/dy - dEy/dx = Bdot (this comes from curl E = Bdot)
dEx/dx + dEy/dy = 0 (this comes from div E = 0)
and cannot figure out which elements in the beta matrix to fill in. It seems like there should be only four elements, not eight! The four elements should correspond to the coefficients of dEx/dx, dEx/dy, dEy/dx, and dEy/dy.
What gives?