The main goal of this investigation was that of developing suitable two- and threedimeminnal
computer codes, which would remain open to the possibility of including
additional physics and more powerful methods for consistently tackling the problem
of protostellar collapse and fragmentation into multiple stellar systems. In Chapter 2,
we discuss the relevant physical situations presumably encountered during the early
star formation phase. A discussion is also given of the central problem regarding angular
momentum transfer during the protostellar collapse. In Chapter 3, we comment
on the physical assumptions made and present the basic differential equations as well
as the initial and boundary conditions necessary for obtaining numerical solutions of
these equations. The description of the computational grid is given in Chapter 4. The Poisson solver is together with tests of its accuracy fully described in Chapter 5. Chapter
6 is entirely devoted to the hydrodynamical approximation and the development
of the codes. In Chapter I 1 we discuss the results obtained for spherically symmetric
collapse and, in Chapter 8, we describe the phenomenon of ring formation as it has
been observed with the 2-dimensional axisymmetric code. Finally, Chapter 9 contains
brief comments on further lines of work. Three appendices have also been included.
Appendix A gives details of the Poisson solver implemented for the 2-dimensional calculations.
In Appendix B, we illustrate a root-finding algorithm for the zeros of the
Legendre polynomials of odd degree, which are used in determining the structure of
the grid along the 0-direction. In Appendix C, we conclude by giving the basic forms
of the finite-difference replacements used in the discretization of the Poisson equation
and the equations of motion.
