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 O(δt 2) convergence in the L 2 norm of the velocity for both variants. We also prove O(δt 3/2) convergence in the H 1 norm of the velocity and the L 2 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].
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