Evaluation of the Artificial Compressibility Method for the Solution of the Incompressible Navier-Stokes Equations

Abstract

The numerical solution of the Navier-Stokes equations for an incompressible fluid still represents a computational challenge. The main reason is due to the lack of an equation for the pressure which makes the coupling between the velocity field and the pressure field a bit mysterious (see the abstract of Gresho and Sani [1] for a description of the mystery). In thé late sixties and the early seventies several pressure-velocity coupling procedures were proposed [2, 3, 4]. Surprisingly, the underlying philosophy of each procedure remained unchanged since their introduction, and almost all the methods employed today for solving the incompressible Navier-Stokes equations used one of these coupling procedures. Furthermore, the question “which pressure-velocity coupling procedure is the most suited for the numerical simulation of incompressible flows” is still debated between the antagonist churches. The purpose of the present work is to contribute to the debate by a quantitative evaluation of the artificial compressibility method. Before discussing in details the investigations performed, the numerical method will be described briefly.