Modelling the solar magnetism: from its internal origin to its manifestations at the surface

This thesis is part of the general study of dynamical processes involved in stars such as convection, rotation or magnetic fields and of their nonlinear interactions. The results of numerical simulations using the 2D finite element code STELEM and the pseudo-spectral 3D code ASH are presented. The first part of this work focuses on the global modeling of the solar dynamo. Through 2D simulations using mean-field theory, I studied the influence of a complex profile of meridional flow in Babcock-Leighton models. We show that there may be doubts about the ability of such models to reproduce the main characteristics of the solar cycle. In order to better constrain the effects of solar variability on the Earth climate, we present a first application in solar physics of sophisticated prediction methods which are used in meteorology. I also computed the first 3D MHD simulations in spherical geometry of a key step in the solar dynamo: the nonlinear evolution of magnetic structures from the base of the convection zone up to the surface where they produce active regions. Weak fields are likely to be modulated by convective motions, thus creating favored longitudes of emergence. If these structures are sufficiently arched, the orientation of bipolar spots corresponds to Joy's law. The introduction of an atmosphere in these models is a step towards a 3D global vision of our Sun. (author)