Summary: TEMPORAL SECOND-ORDER ACCURACY OF
SIMPLE-TYPE METHODS FOR INCOMPRESSIBLE
UNSTEADY FLOWS
Ming-Jiu Ni and Mohamed A. Abdou
UCLA MAE Department, Engineering IV,
Los Angeles, California, USA
SIMPLE-type 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 SIMPLE-type methods have second-order temporal accuracy if a
second-order 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 second-order updating techniques are presented. A classical validation example
is employed to validate the temporal accuracy in this article. A new four-step SIMPLE-type
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

Source: Abdou, Mohamed - Fusion Science and Technology Center, University of California at Los Angeles

Collections: Plasma Physics and Fusion