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Solution of the gravitational poisson equation in spherical coordinates

✍ Scribed by M. Claudius

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
748 KB
Volume
27
Category
Article
ISSN
0010-4655

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✦ Synopsis

Methods for solving the gravitational Poisson equation in spherical coordinates (2 and 3 series dimensions) are discussed with special reference to proto-star collapse calculations. Two different methods, both using expansion of the potential into Legendre functions, are described. The methods have been programmed for the 2-dimensional case with rotational symmetry and reflective equatorial symmetry. They have been tested on some density distributions relevant to collapse simulations and are found to be both fast and accurate.

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The solutions of the Poisson equation in regular and irregular shaped physical domains are obtained by the cubature method. The solutions of the three test problems involving regular shaped domains are compared with the analytical solutions and the control-volume, ®ve-point ®nite dierence, Galerkin