[CIG-CS] Gamr status

[Walter Landry]

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