  In fluid dynamics, an important problem is linked to the knowledge of the
fluid pressure. Recently, another approach to study incompressible fluid flow
was suggested. It consists in using a general pressure equation (GPE) derived
from compressible Navier-Stokes equation. In this paper, GPE is considered and
compared with the Chorin's artificial compressibility method (ACM) and the
Entropically damped artificial compressibility (EDAC) method. The three methods
are discretized in a staggered grid system with second order centered schemes
in space and a third order Runge-Kutta scheme in time. Three test cases are
realized: two-dimensional Taylor-Green vortex flow, the traveling wave and the
doubly periodic shear layers. It is demonstrated that GPE is accurate and
efficient to capture the correct behavior for unsteady incompressible flows.
The numerical results obtained by GPE are in excellent agreement with those
obtained by ACM, EDAC and a classical finite volume method with a Poisson
equation. Furthermore, GPE convergence is better than ACM convergence. The
proposed general pressure equation (GPE) allows to solve general, time-accurate
, incompressible Navier-Stokes flows. Finally, the parametric study realized in
terms of Mach and Prandtl numbers shows that the velocity divergence can be
limited by an arbitrary maximum and that acoustic waves can be damped.
