PolarCELL SOON AVAILABLE
Potential and acceleration in a homogeneous polar cell
J.M. Huré (Université Bordeaux 1 & LAB/OASU) — 2009, april

Email : jean-marc.hure@obs.u-bordeaux1.fr
Web page : www.obs.u-bordeaux1.fr/radio/JMHure/intro2polarcell.html

  What is it ?

PolarCELL.

The code is easy-to-use; it is written in Fortran 90 (with no external dependancies).
The code works under variable precision.

Current version: PolarCELL V1, 2009, april

  Reference

Huré J.-M., Pierens A., & Hersant F., 2009,
"Self-gravity at the scale of the polar cell",
Astronomy & Astrophysics Let., submitted for publication

Abstract. We present the exact calculus of the gravitational potential and acceleration along the symmetry axis of a plane, homogeneous polar cell as functions of mean radius a, radial extension Δa and opening angle Δφ. Accurate approximations are derived in the limit of high numerical resolutions at the geometrical mean α of the inner and outer radii (a key-position in current FFT-based Poisson solvers). Our results extend to all resolutions the approximate formula given in Binney & Tremaine (1987) corresponding to the singular term and definitely clarify the question about the existence (or not) of self-forces in polar cells. Indeed, we found that there is always a self-force at radius α except if the shape factor aΔφ/Δa is or the order of 3.531, asymptotically. A polar mesh made with such cells is therefore especially well suited to high resolution simulations of self-gravitating media in two dimensions. A by-product of this study is a newly discovered indefinite integral involving complete elliptic integral of the first kind over modulus.

→ for more details, see Huré, Pierens, Hersant, 2009, A&A (submitted)

  Properties and typical calling sequence

Precision : single, double or quadruple.
Computing time : linear with the expansion order.
Reliability : potential is finite everywhere; no singularities.
Accuracy : computer precision reachable with a few orders inside and outside the disc (more terms are need at the disk edges; see the graphical examples).

Typical F90 calling sequence for PolarCELL V1: 2009, april (current version):

  Copyright


PolarCELL is protected according to the terms and conditions of the GNU General Public License.

  Credits

If you use PolarCELL, please cite the following reference : Huré, Pierens, Hersant, 2009

  Portability and optimization

In principle, PolarCELL is fully portable and requires no external libraries.

The code is not optimized. Depending on applications, computing time can be saved by specific recoding.

  Versions

  Graphical examples

  Download, install and run PolarCELL

That's all, in principle.
Feel free to change the input parameters (at you own risk!).

Please, contact me if problems or questions.