Protostellar Collapse Models: Development of a Multi-Dimensional Numerical Code

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.