imposing symmetric boundary conditions on the axis of symmetry of a 2D domain

[tzgo...@gmail.com]

Dear all,

      Recently I'm working on the phase-field simulation of dendritic growth by deal.II and I want to make the simulation carried out on only half of the domain due to the symmetry of the problem with respect to the vertical axis to improve computational efficiency. So how to impose such sysmmetric boundary conditions on the axis of symmetric of a 2D comptation domain?

[Wolfgang Bangerth]

That depends on the equation and on what you actually want to do. Do you
have a 2d domain and only want to simulate half of it, or a 3d
axisymmetric domain for which you only want to simulate in r-z space?

Best
W.

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

[Tongzhao Gong]

Hi Bangerth,

      Thanks for your answering. Here I have a 2D domain and the phase-field model is complicated, so I have simplify the equations just like as follow: 

      For both variable \phi and u, zero-flux Neumann boundary conditions are imposed. Owing to the symmetic domain like the following picture, I want to just computation on half of the domain and the results can be mirrored to the other half. However, I have no idea on how to impose the symmetric boundary condition on the y-axis if I only use half of the whole domain to carry out the simulation. For example, the whole domain is a square whose center is located at origin, here I just computation on the domain satisfying x > 0 and the symmetric boundary condition should be imposed on the boundary satisfying x = 0.

在 2017年3月28日星期二 UTC+8上午2:38:20，Wolfgang Bangerth写道：

[Stephen DeWitt]

In that case, you should just be able to use zero-flux boundary conditions along the mirror plane. The way I typically picture it is that if you have the same thing happening on either side of a mirror plane, you can't have in-flow or out-flow. 

On a side note, depending on how far along you are on your code development, we have a general phase field code built on deal.II called PRISMS-PF, that you might be interested in. Our GitHub repo is here, and feel free to email me at stv...@umich.edu if you have any questions about it.

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Steve

[Tongzhao Gong]

Thanks, DeWitt.

在 2017年3月29日星期三 UTC+8上午1:50:16，Stephen DeWitt写道：