Accurate Projection Methods for the Incompressible Navier–Stokes Equations

Brown, David L.; Cortez, Ricardo; Minion, Michael L.

doi:10.1006/jcph.2001.6715

Accurate Projection Methods for the Incompressible Navier–Stokes Equations

Journal Article · Tue Apr 10 00:00:00 EDT 2001 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.2001.6715· OSTI ID:1429358

Brown, David L. ^[1]; Cortez, Ricardo ^[2]; Minion, Michael L. ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
Tulane Univ., New Orleans, LA (United States). Dept. of Mathematics
Univ. of North Carolina, Chapel Hill, NC (United States). Dept. of Mathematics

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_∞-norm. Here, we identify 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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: Alfred P. Sloan Foundation; National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC02-05CH11231; FG02-92ER25139; W-7405-ENG-36; W-7405-ENG-48

OSTI ID:: 1429358

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 168; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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