[CIG-CS] Particle problems and Semi-Lagrangian Schemes for Gamr

[Walter Landry]

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mspieg <mspieg at ldeo.columbia.edu> wrote:
> Hi Walter,
>   Mike is quite right, I've been using Semi-Lagrangian methods for ages in
> both finite volume, and more recently finite element calculations.  They have
> a lot of nice properties, but can be computationally expensive in elements
> (depending on how they're implemented).  However, because they advect
> continuous fields, they will scale linearly with your degrees of freedom (or
> possibly quadrature points) (and they don't have CFL stability issues).

This is very interesting.  What do you mean that they are expensive in
elements?  I would expect the cost of advection would be dwarfed by
the cost of solving Stokes.

Also, I found Katz et. al. [1], which includes a mid-ocean ridge
model.  That uses finite volumes.  Do you have any results for a
finite-element semi-lagrangian scheme I can look at?

> I actually have a demonstration T-Dependent viscosity Rayleigh-Benard problem
> with semi-lagrangian advection implemented in hybrid FEniCS/PETSc codes if
> you're interested.

Cheers,
Walter Landry
walter at geodynamics.org


[1] Numerical simulation of geodynamic processes with the Portable
    Extensible Toolkit for Scientific Computation
    R.F. Katz, M.G. Knepley, B. Smith, M. Spiegelman, E.T. Coon,
    Physics of the Earth and Planetary Interiors 163 (2007) 52$(Q#|(B68