 
Summary: TEMPORAL SECONDORDER ACCURACY OF
SIMPLETYPE METHODS FOR INCOMPRESSIBLE
UNSTEADY FLOWS
MingJiu Ni and Mohamed A. Abdou
UCLA MAE Department, Engineering IV,
Los Angeles, California, USA
SIMPLEtype methods are presented in a more concise formulation. This formulation is
used to analyze temporal accuracy for unsteady flows. Detailed error formulations are
given. Analysis shows that SIMPLEtype methods have secondorder temporal accuracy if a
secondorder temporal updating technique is employed to update both the convective and
diffusion terms. Two algorithms for unsteady flows are presented. Algorithm A is an
iteration method, which will cost more time than algorithm B, a noniteration algorithm.
Also several secondorder updating techniques are presented. A classical validation example
is employed to validate the temporal accuracy in this article. A new fourstep SIMPLEtype
method is presented, in which the pressure Poisson equation, not the pressure difference
Poisson equation is solved.
1. INTRODUCTION
The dimensionless unsteady incompressible NavierStokes equations in
primitive variables can be written as
@u
