[Carpetx-developers] lapse terms in Whisky's fluxes

[Erik Schnetter]

(To clarify, I am not one of the original authors of Whisky.)

-erik

On Tue, Oct 19, 2021 at 3:01 PM Roland Haas <rhaas at illinois.edu> wrote:
>
> Hello Ian,
>
> While working on a hydro code for CarpetX the people involved (in cc
> via the mailing list) ran into the issue of how to handle the lapse the
> show up in the flux of the fluid equations.
>
> E.g. in GRHydro (nee Whisky) one uses a numerical flux of (say for D)
> in
> https://www.einsteintoolkit.org/thornguide/EinsteinEvolve/GRHydro/documentation.html#x1-80003
>
> as F^i_D = D (\alpha v^i - \beta^i) yet the flux expressions used in
> the Riemann problem are computed as:
>
> \tilde F^i_D = D (v^i - \beta^i/\alpha)
>
> ie a factor of the lapse has been divided out.
>
> It gets put back when the fluxes are combined to compute a right hand
> side by using:
>
> RHS = \alpha_{i-1/2} F^j(x_{i-1/2}) - \alpha_{i+1/2} F^j(x_{i+1/2})
>
> None of the CarpetX developers (with the possible exception of Erik,
> but his expertise is in a different area and in any case he does not
> remember) were involved in the original Whisky code.
>
> So: do you remember if there was a specific reason why the lapse was
> divided out in the expressions used in the Riemann problem?
>
> Yours,
> Roland
>
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-- 
Erik Schnetter <eschnetter at perimeterinstitute.ca>
http://www.perimeterinstitute.ca/personal/eschnetter/