Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2007; 72:1490­1512
Published online 2 May 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2054
A bridge between projection methods and SIMPLE type methods
for incompressible Navier­Stokes equations
Ming-Jiu Ni, and Mohamed A. Abdou
Mechanical and Aerospace Engineering Department, University of California at Los Angeles,
Los Angeles, CA 90095, U.S.A.
SUMMARY
A bridge is built between projection methods and SIMPLE type methods (Semi-Implicit Method for
Pressure-Linked Equation). A general second-order accurate projection method is developed for the
simulation of incompressible unsteady flows by employing a non-linear update of pressure term as
n
pn+1 + (I - n
) pn, where n
is a coefficient matrix, which may depend on the grid size, time
step and even velocity. It includes three- and four-step projection methods. The standard SIMPLE method
is written in a concise formula for steady and unsteady flows. It is proven that SIMPLE type methods have
second-order temporal accuracy for unsteady flows. The classical second-order projection method and
SIMPLE type methods are united within the framework of the general second-order projection formula.

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

Collections: Plasma Physics and Fusion