Houjun:
Indeed my question is not that clear. The upper panel is actually a
'potential' (phi, solving a Poisson's equation), the lower panel is the
x-component of ExB (E=-\nabla phi, B is out of paper), a derivative quantity.
This ExB would be used to transport plasma density, (and this plasma density
field is then feedback to Poisson's equation through rhs and coef.).
The relevant literatures assume different kinds of BCs, e.g., Neumann for both
potential and plasma density in y (one mentioned extrapolation too) and
periodic in x. Those simulations usually show a good symmetry in x, but mine
shows asymmetry quickly near the top boundary. Although we'll be mainly
interested in what'll happen in the interior, this boundary is a nuisance.
Don't know how you can enforce \partial rho (density) / \partial y = 0 at the
top boundary directly in the transport equation, except modifying the flow
field near the boundary?
I think you already fixed the problem, but as a general rule: The questions
you ask, namely which boundary condition to choose, is not a mathematical one.
It is one of modeling the system you want to simulate. What boundary condition
is appropriate depends on what system you try to describe, not whether the
results of a simulation appear right or wrong, or convenient or not.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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