[Users] McLachlan with shift advection but centred stencils

Erik Schnetter schnetter at cct.lsu.edu
Mon Apr 11 13:49:38 CDT 2016

Roland

This is currently no implemented. There are currently two choices for
calculating "upwind" derivatives (i.e. the shift-related spatial part
of the Lie derivatives):

If[splitUpwindDerivsKranc,
Upwind[dir_, var_, idx_] := dir PDua[var,idx] + Abs[dir] PDus[var,idx],
Upwind[dir_, var_, idx_] := dir PDu[var,idx]];

By setting

Upwind[var_,dir_,idx_] = PD[var,idx];

you can change these "upwind" derivatives to be identical to regular
derivatives. This happens at the level of Mathematica, before the
equations are passed to Kranc, so that you will need one less ghost
zone.

I would be happy to add a respective parameter to the Kranc script.
For performance reasons this can't be a run-time parameter, though.

Note that this is always possible with the BSSN equations -- this is
not a question of stability. We are using upwind derivatives since
Peter Diener (?) found out that these lead to more accurate binary
black hole evolutions, compared to centred differences.

-erik

On Sun, Apr 10, 2016 at 3:57 PM, Roland Haas <rhaas at aei.mpg.de> wrote:
> Hello all,
>
> just to be sure (I read McLachlan_BSSN.m but want to be sure): it is
> currently not possible to run a simulation using ML using shift
> advection beta^i\partial_i but without upwinding the advection
> derivatives, is it? Such an option is useful for simulations without
> black holes where one can potentially safe a ghost zone by using only
> centred stencils.
>
> Yours,
> Roland
>
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Erik Schnetter <schnetter at cct.lsu.edu>
http://www.perimeterinstitute.ca/personal/eschnetter/