# Projecting Solutions for Axisymmetric Flow

**URL:** https://fenicsproject.discourse.group/t/projecting-solutions-for-axisymmetric-flow/5555
**Category:** Uncategorized
**Created:** [April 9, 2021, 6:50pm UTC](https://fenicsproject.discourse.group/t/projecting-solutions-for-axisymmetric-flow/5555 "2021-04-09T18:50:37Z")
**Posts on this page:** 5
**Page:** 1

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### Author: ![bcu](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/bcu/32/1872_2.png) [@bcu](https://fenicsproject.discourse.group/u/bcu)
#### Post date: [April 9, 2021, 6:50pm UTC](https://fenicsproject.discourse.group/t/projecting-solutions-for-axisymmetric-flow/5555/1 "2021-04-09T18:50:37Z")

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Hello,

Is there a way to project a solution from half of a rectangular domain into the other half of the domain? To reduce the computational cost of solving for the full domain of Axisymmetric Navier stokes equations in 2D, I’d like to only solve for half of the domain and project the solutions to the other half since it is axisymmetric. Please let me know if this is possible in FENICS.

 ![image](https://global.discourse-cdn.com/free1/uploads/fenicsproject1/original/2X/4/4b838d725dccace57865f2eaae0f7be4906e721f.png)

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### Author: ![bleyerj](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/bleyerj/32/6020_2.png) [@bleyerj](https://fenicsproject.discourse.group/u/bleyerj)
#### Post date: [April 9, 2021, 8:39pm UTC](https://fenicsproject.discourse.group/t/projecting-solutions-for-axisymmetric-flow/5555/2 "2021-04-09T20:39:06Z")

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Here is an [example of axisymmetric computations in solid mechanics](https://comet-fenics.readthedocs.io/en/latest/demo/elasticity/axisymmetric_elasticity.html)

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<div class="post-metadata">

### Author: ![bcu](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/bcu/32/1872_2.png) [@bcu](https://fenicsproject.discourse.group/u/bcu)
#### Post date: [April 12, 2021, 1:16am UTC](https://fenicsproject.discourse.group/t/projecting-solutions-for-axisymmetric-flow/5555/3 "2021-04-12T01:16:56Z")

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Thanks, Bleyerj. Yes, I have seen this before. One thing that I have questions about is how to apply the boundary conditions. For example, if I only use the top half of the domain, what sort of boundary condition do I give the axis at which the symmetry occurs (if at all)?

 ![image](https://global.discourse-cdn.com/free1/uploads/fenicsproject1/original/2X/a/aea4928ae6f9564d5a7c463563a3d298401f10b5.jpeg)

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<div class="post-metadata">

### Author: ![bleyerj](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/bleyerj/32/6020_2.png) [@bleyerj](https://fenicsproject.discourse.group/u/bleyerj)
#### Post date: [April 12, 2021, 12:59pm UTC](https://fenicsproject.discourse.group/t/projecting-solutions-for-axisymmetric-flow/5555/4 "2021-04-12T12:59:36Z")

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You can apply a slip boundary condition u\_y=0 on the symmetry axis

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<div class="post-metadata">

### Author: ![bcu](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/bcu/32/1872_2.png) [@bcu](https://fenicsproject.discourse.group/u/bcu)
#### Post date: [April 12, 2021, 1:58pm UTC](https://fenicsproject.discourse.group/t/projecting-solutions-for-axisymmetric-flow/5555/5 "2021-04-12T13:58:23Z")

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Thanks again. Forgive me if this is a simple implementation but I don’t have experience implementing slip bcs. For the previous full domain, I had a no-slip BCs in my code using the following:

> u\_ZERO = Constant((0.0,0.0))  
> bc\_noslip = DirichletBC(W.sub(0), u\_ZERO, domainBoundaries, ID\_BOTTOM)

How can I make it a slip condition as you mentioned? I can set u\_y = 0 but what about u\_x?