Extrapolation to the boundary

[Houjun Wang]

Hi, 

Is there any way to 'extrapolate' the field (from interior to the boundary) such that the lower panel looks like the upper panel near the top boundary? Or enforcing zero normal gradient near the top boundary for the bottom panel too. Thanks.

Houjun

[Wolfgang Bangerth]

On 4/14/23 14:46, Houjun Wang wrote:
>
> Is there any way to 'extrapolate' the field (from interior to the boundary)
> such that the lower panel looks like the upper panel near the top boundary? Or
> enforcing zero normal gradient near the top boundary for the bottom panel too.

Houjun,
I understand intuitively what you want, but in the end, in order to implement
something, you have to specify clearly and unambiguously in mathematical terms
what it is you want to do. So before we talk about how, can you clarify what
achieving "looks like the upper panel" would entail?

As for Neumann boundary conditions: You would first have to tell us how you
have computed the two panels, and then think about whether it makes sense from
a modeling perspective to choose one type of boundary conditions over another.

Best
Wolfgang

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Houjun Wang]

Thanks, Wolfgang. 

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?

Any suggestions? Thanks again.

Houjun

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[Houjun Wang]

BTW, the asymmetry mentioned in my previous email is due to my mistake in transport implementation; with that gone I can experimented about boundary conditions if necessary. Thanks the same.  

[Wolfgang Bangerth]

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.