The main objective of this thesis is to accelerate deflated Conjugate Gradient solvers used for solving the pressure Poisson equation, for the simulation of low-Mach number flows on unstructured meshes. A restart method based on an estimation of the effect of numerical errors has been implemented and validated. Then, a three-level deflation method has been created, and two techniques are developed in order to reduce the number of iterations on the coarse levels : one of them is the creation of initial guesses thanks to a well-suited projection method, the other one consists in adapting the convergence criterion on the coarse grids. Numerical results on massively parallel simulations show, among others, a drastic reduction of the computational times of the solver. Other lines of research are introduced, especially regarding dynamic load balancing.
