Hi Wolfgang

It seems that the NS equation solver in this gallery code is based on 
projection method. The continuous Galerkin Finite Elements with high-order 
stabilization is used for the level set solver though. 

How hard would it be to first extend Step-57 to be non-steady, and then add 
stabilization terms? My main concern is whether Newton iteration + FGMRES 
approach remains the same.

Thank you
Jie

On Tuesday, October 3, 2017 at 11:37:34 PM UTC-4, Wolfgang Bangerth wrote:
>
>
> Jie, 
>
> > I am working on an incompressible Navier-Stokes solver which may later 
> be 
> > extended to slightly compressible solver. The flow of interest could 
> sometimes 
> > be convection-dominated so I would like to use Petro-Galerkin 
> stabilization 
> > method, specifically, the streamline-upwind Petrov Galerkin (SUPG) 
> method. 
> > 
> > There are already a few tutorials on solving Navier-Stokes equations, 
> but none 
> > of them uses stabilization method. I started learning deal.ii a month 
> ago and 
> > I still don't feel comfortable writing such a complicated program from 
> > scratch. So I wonder if anyone has done similar things. Any suggestions 
> on how 
> > to solve the resulting matrix system of SUPG method are also welcome. 
>
> I think you want to look at this code gallery program: 
>    
> https://dealii.org/developer/doxygen/deal.II/code_gallery_two_phase_flow.html 
>
> It's a large program, so it may not be easy to read through, but I am 
> pretty 
> sure that it uses stabilization for the N-S equations. 
>
> Best 
>   W. 
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 bang...@colostate.edu 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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