Protostellar formation in rotating interstellar clouds. I - Numerical methods and tests

Attention is given to numerical methods and tests of a series of gravitational hydrodynamics computer codes constructed in order to numerically follow the dynamic collapse of spherically symmetric (1-D), axisymmetric (2-D), and non-axisymmetric (3-D) isothermal interstellar clouds. A spherical harmonic expansion is used to solve the Poisson equation for the gravitational potential. It is shown that the use of explicit donor-cell hydrodynamics on a moving spherical coordinate grid ensures mass and momentum conservation and allows the grid to follow the collapse of the fluid. Finally, the performance of the codes is examined.