Quelques résultats nouveaux sur les méthodes de projection

Abstract

We revisit fractional step projection methods for solving the Navier–Stokes equations. We study a variant of pressure-correction methods and introduce a new class of velocity-correction methods. We prove stability and $\text{O}\text{(δt}{}^2\text{)}$ convergence in the L² norm of the velocity for both variants. We also prove $\text{O}\text{(δt}{}^{\mathrm{3/2}}\text{)}$ convergence in the H¹ norm of the velocity and the L² norm of the pressure. We show that the new family of projection methods can be related to a set of methods introduced in [4,3]. As a result, this Note provides the first rigorous proof of stability and convergence of the methods introduced in [4,3].