On the Accuracy of the Splitting Schemes for Incompressible Flows

Abstract

In this talk, we will review various splitting schemes for solving time dependent Navier-Stokes equations. These schemes share the same advantage that one only needs to solve a sequence of decoupled Poisson-type equations at each time step and have been widely used in practice due to their efficiency and simplicity. However, since the splitting involves non-commutative operators, how to design accurate and stable splitting schemes is a very subtle issue.  We will present error estimates for two class of splitting schemes, namely pressure-correction and velocity-correction schemes and show that they all suffer from an irreducible splitting error. We will then present a new class of truly consistent splitting schemes.  Finally, we will discuss the influence of open boundary conditions on the accuracy of the splitting schemes.