[CIG-CS] Gamr status
Walter Landry
walter at geodynamics.org
Mon May 23 17:32:21 PDT 2011
Walter Landry <walter at geodynamics.org> wrote:
> Greetings Everyone,
>
> The SAMRAI based finite difference Stokes solver is working, so I have
> tried out the Sinker benchmark for both. It turns out that they both
> break down even for more moderate viscosity jumps (10^2). The problem
> is that the discretisation can not represent sharp viscosity jumps.
> So if you tell the code to keep refining where the error is, the code
> will refine all the way to zero cell size. I have attached pictures
> of the pressure in 2D and 3D for both codes.
One possible solution for this for finite elements is XFEM. Zlotnik
et. al. [1] used XFEM and level sets for Stokes in slab subduction in
2D. I am a bit puzzled by their test results. The max relative
errors are only reduced by a factor of 2, which seems unimpressive.
Zlotnik and Díez [2] extended the method to multiphase and 3D. Rather
than contending with the geometrical complexities involved when
cutting elements with more than one interface, so they used a simple
integration scheme. Unfortunately, that meant that they had to use an
adaptive mesh that is concentrated at the interfaces.
Cheers,
Walter Landry
walter at geodynamics.org
[1] Sergio Zlotnik, Pedro Dıez, Manel Fernandez, Jaume Verges,
Numerical modelling of tectonic plates subduction using X-FEM,
Comput. Methods Appl. Mech. Engrg. 196 (2007) 4283–4293
[2] Sergio Zlotnik, Pedro Díez, Hierarchical X-FEM for n-phase flow (n
> 2), Comput. Methods Appl. Mech. Engrg. 198 (2009) 2329–2338
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