Abstract
One of the priorities of contemporary astrophysics remains to understand the mechanisms which lead to star formation. In the dense cores where star formation occurs, temperature, pressure, etc... are such that it is impossible to reproduce them in the laboratory. Numerical calculations remain the only mean to study physical phenomena that are involved in the star formation process. The focus of this thesis has been on the numerical methods that are used in the star formation context to describe highly non-linear and multi-scale phenomena. In particular, I have concentrated my work on the .rst stages of the prestellar dense cores collapse.
This work is divided in 4 linked part. In a .rst study, I use a 1D Lagrangean code in spherical symmetry (Audit et al. 2002) to compare three models that incorporate radiative transfer and matter-radiation interactions. This comparison was based on simple gravitational collapse calculations which lead to the .rst Larson core formation. It was found that the Flux Limited Di.usion model is appropriate for star formation calculations. I also took bene.t from this .rst work to study the properties of the accretion shock on the .rst Larson core. We developed a semi-analytic model based on well-known assumptions, which reproduces the jump properties at the shock. The second study consisted in implementing the Flux Limited Di.usion model with the radiation-hydrodynamics equations in the RAMSES code (Teyssier 2002). After a .rst step of numerical tests that validate the scheme, we used RAMSES to perform the .rst multidimensional collapse calculations that combine magnetic .eld and radiative transfer e.ects at small scales with a high numerical resolution. Our results show that the radiative transfer has a signi.cant impact on the fragmentation in the collapse of prestellar dense cores. I also present a comparison we made between the RAMSES code (Eulerian approach) and the SPH code DRAGON (Goodwin 2004, Langrangean approach). We studied the e.ect of the numerical resolution on the angular momentum conservation and on the fragmentation. We show that the two methods converge, provided that we use high numerical resolution criteria, which are much greater than the usual criteria found in the literature. The two methods then seem to be adapted to the study of tar formation.