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

[Klaus Weide]

On Mon, 22 Dec 2014, Rodrigo Fernandez wrote:

> Dear FLASH Users,
> 
> I'm writing to document the changes to the public FLASH3 distribution
> needed to enable the split PPM hydro solver to work in 3D spherical polar
> coordinates. I've been told that a number of people are interested in this
> functionality. Since I've done some debugging and testing of this myself, I
> thought that the results would be useful to those interested.

Rodrigo,

Thank you for sending this.

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.


I have a question related to your last point:

> 6) In addition, users should be aware that the split PPM solver
> reconstructs in the coordinate, not in volume. This is OK for coordinates
> with invariant transverse area (e.g. cartesian), but not for others like
> spherical radius. Nevertheless, at high enough resolution the correct
> behavior is obtained asymptotically, e.g. for spherical radius:
> 
>       R_R^3 - R_L^3 = 3*R_C^2 * DR * ( 1 + [DR/R_C]^2/12 )
> 
> Where R_R, R_C, and R_L refer to right, centered, and left radial
> coordinate, respectively, and DR = R_R - R_L.

> Users should make sure that the resolution is good enough for the code to
> converge to the right answer within some tolerance, by e.g. carrying out
> tests with known solutions.

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?


(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!)

Klaus