Jie Shen
Department of Mathematics, Purdue University
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.
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