Problem with ALE formulation of Navier-Stokes

Numerical methods and mathematical models of Elmer
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diana.carlson
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Joined: 21 Oct 2009, 09:49

Problem with ALE formulation of Navier-Stokes

Post by diana.carlson »

Hi there
I still have problems with ALE formulation used for solving flow equations in Elmer. Let me explain via an example, (i.e. Tutorial 16: Fluid flow around an elastic beam). The problem is steady-state so the ‘compute mesh velocity’ option is not active and the mesh velocity is zero. So in ‘NavierStokesCompose’ subroutine the mesh velocity is taken to be zero and the flow problem is essentially solved in Eulerian (not ALE) framework. On the other hand the mesh is displaced in every time step and we have an updated mesh that I name it ‘new mesh’ in comparison to the ‘old mesh’ which we had at the start of the time step. Thus the mesh has changed from the old to the new one during the time step while the problem is solved in Eulerian and not ALE formulation, so the variables should be mapped from the ‘old mesh’ to the ‘new mesh’, but I can’t find such a mapping in associated subroutines. Is there anything that I didn’t account for it or it’s another bug?
Thanks,
Diana Carlson, NY
raback
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Re: Problem with ALE formulation of Navier-Stokes

Post by raback »

Hi Diana

Indeed, there is no mapping of previous values in steady state analysis. However, in steady state there should neither be reference to the previous pressure or velocity values except in nonlinear terms and due to relaxation. However, even these should be the same when convergence is reached. And also the virtual mesh velocity should vanish when convergence is reached. So I do not see where consistency would be broken.

One could of course speculate whether improved convergence would be obtained if values would be mapped from the previous geometric configuration. Even this I doubt since the mapped velocity field does not honor the Dirichlet BCs while the unmapped field automatically does. Thus, particularly for large deformations the interpolation or extrapolation could give rather poor approximations near the boundary.

-Peter
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