A volume penalization method for the simulation of magnetohydrodynamic (MHD) flows in confined domains is presented. Incompressible resistive MHD equations are solved in 3D by means of a parallelized pseudo-spectral solver. The volume penalization technique is an immersed boundary method, characterized by a high flexibility in the choice of the geometry of the considered flow. In the present case, it allows the use of conditions different from periodic boundaries in a Fourier pseudo-spectral scheme. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamical and MHD flows by comparing the numerical results with those of the literature or analytical solutions. Then, the spontaneous generation of kinetic and magnetic angular momentum is studied for confined 2D and 3D MHD flows. The influence of the Reynolds number and of the ratio of kinetic/magnetic energies is explored, as well as the differences induced by the boundary conditions. The fact that axisymmetric borders introduce a non-zero pressure term in the evolution equation of the angular momentum is essential to generate large values of the angular momentum. It is investigated whether this self-organization is exclusively observed in 2D flows by considering 3D MHD in the presence of a strong axial magnetic field. The last part is devoted to the simulation of a conducting fluid in a periodic cylinder with imposed axial and poloidal magnetic forcing, implying a resulting magnetic field. By varying the amplitude of the poloidal forcing, different dynamical states can be achieved. The effect of the Prandtl number on the threshold of the instabilities is then studied.

In this thesis we developed a Fourier pseudo-spectral code coupled with the volume penalization for the simulation of turbulent MHD flows with non-periodic boundary conditions. This method was validated with classical and academic test-cases. Then we studied the influence of the confinement with walls in a 2D configuration for decaying MHD and we found four decaying regimes which depend on the initial conditions. We also discussed the phenomenon of spontaneous rotation, or spin-up, in 2D non-axisymmetric geometries, originally discovered in hydrodynamic flows. We showed the influence of the Reynolds number and the magnetic pressure on this phenomenon. Finally, simulations of MHD flows in wall bounded three-dimensional domains were addressed. The first results concerning the simulation of decaying MHD turbulence in a cylinder imposing Dirichlet boundary conditions for both the velocity and the magnetic field showed the validity of the code and suggest good prospects for developing more physically justified boundary conditions for the magnetic field.