Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 168, Issue 2, Pages 464-499Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jcph.2001.6715
Keywords
incompressible flow; projection method; boundary conditions
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This paper considers the accuracy of projection method approximations to the initial-boundary-value problem for the incompressible Navier-Stokes equations. The issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second-order methodology a decade and a half ago. It has been observed that while the velocity can be reliably computed to second-order accuracy in time and space, the pressure is typically only first-order accurate in the L-infinity-norm. This paper identifies the source of this problem in the interplay of the global pressure-update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second-order accurate, as demonstrated by a normal mode analysis and numerical experiments. In addition, a numerical method based on a gauge variable formulation of the incompressible Navier-Stokes equations, which provides another option for obtaining fully second-order convergence in both velocity and pressure, is discussed. The connection between the boundary conditions for projection methods and the gauge method is explained in detail. (C) 2001 Academic Press.
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