[FLASH-USERS] using the split PPM hydro solver in 3D spherical polar coordinates

[Rodrigo Fernandez]

Klaus,


> I intend to apply your changes to the FLASH code base, so they can be
> included in the next FLASH release if no unexpected problems show up.
>

Thank you for your response and for being willing to add this to the public
distribution.



> There is code in states.F90 that takes geometry into account (lines
> related to 'dloga'). Have you considered those "corrections" to states "to
> include geometry terms"?  Do they address part of your concern?
>

My understanding is that those terms are there to correct the domain of
dependence for geometry when computing the 'modified states' for the
Riemann solution.

The point about the reconstruction is a separate one. For consistency with
the Eulerian formulation of the hydrodynamic equations in conservative
form, the PPM polynomial that yields the first guess at the zone interface
value should assume that the independent coordinate $\xi$ is the volume.
Otherwise the interface value does not arise out of volume-average values.

Colella & Woodward (1984) mention this explicitly in their paper (third
paragraph of section 3) when discussing the Eulerian formulation of PPM. It
just so happens that when using cartesian coordinates, the volume is
proportional to the coordinate.

The subroutine coeff.F90 takes the coordinate increments (dx) as input to
compute the coefficients.

Perhaps someone already thought about this a long time ago and I'm
inventing the wheel here...



> (Of course, users should always make sure the resolution is good enough
> for their purposes, no matter how accurately the methods represents
> something like coordinate-dependent transverse areas in curvilinear
> coordinates!)
>

Agree. The code does give the right answer at sufficiently high resolution,
of that I'm sure because I've tested it in 2D (and recently in 3D). There
is some irreducible level of noise under some circumstances, but nothing
too serious.

Best,

Rodrigo
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