### Abstract

The problem of the self-initiated (due to ambipolar diffusion) formation and contraction of protostellar fragments in model molecular clouds was formulated in a previous paper in axisymmetric geometry, taking advantage of a recent result by Fiedler and Mouschovias; namely, that balance of forces along magnetic field lines is rapidly established and maintained even during dynamic contraction (i.e., collapse) perpendicular to the field lines, at least up to central densities ≃3 × 10^{9} cm^{-3}. We describe a method for solving the reduced, multifluid, nonlinear, magnetohydrodynamic equations that govern the time evolution of such model clouds; algebraic equations for the equilibrium abundances of charged species are solved at each time step. The method consists of an implicit time integrator; an advective difference scheme that possesses the transportive property; a second-order difference approximation of forces inside a cell; an integral approximation of the gravitational and magnetic fields; and an adaptive mesh capable of reliably following the formation and evolution of cloud cores and of resolving length scales smaller than ≃10 AU at densities ≃10^{9} cm^{-3} with only about 100 points to cover the radial extent (typically ≃4.3 pc) of the entire cloud. The accuracy of the method is discussed.

Original language | English (US) |
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Pages (from-to) | 561-569 |

Number of pages | 9 |

Journal | Astrophysical Journal |

Volume | 421 |

Issue number | 2 |

State | Published - Feb 1 1994 |

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### Keywords

- Diffusion
- ISM: magnetic fields
- MHD
- Methods: numerical
- Plasmas
- Stars: formation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*421*(2), 561-569.