Accurate Projection Methods for the Incompressible Navier–Stokes Equations
Abstract
This paper considers the accuracy of projection method approximations to the initial–boundaryvalue 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 secondorder methodology a decade and a half ago. It has been observed that while the velocity can be reliably computed to secondorder accuracy in time and space, the pressure is typically only firstorder accurate in the L_{∞}norm. Here, we identify the source of this problem in the interplay of the global pressureupdate formula with the numerical boundary conditions and presents an improved projection algorithm which is fully secondorder 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 secondorder 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.
 Authors:

 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
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); Alfred P. Sloan Foundation
 OSTI Identifier:
 1429358
 Grant/Contract Number:
 AC0205CH11231; FG0292ER25139; W7405ENG48; W7405ENG36; DMS9816951; DMS9973290
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 168; Journal Issue: 2; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; incompressible flow; projection method; boundary conditions
Citation Formats
Brown, David L., Cortez, Ricardo, and Minion, Michael L. Accurate Projection Methods for the Incompressible Navier–Stokes Equations. United States: N. p., 2001.
Web. doi:10.1006/jcph.2001.6715.
Brown, David L., Cortez, Ricardo, & Minion, Michael L. Accurate Projection Methods for the Incompressible Navier–Stokes Equations. United States. doi:10.1006/jcph.2001.6715.
Brown, David L., Cortez, Ricardo, and Minion, Michael L. Tue .
"Accurate Projection Methods for the Incompressible Navier–Stokes Equations". United States. doi:10.1006/jcph.2001.6715. https://www.osti.gov/servlets/purl/1429358.
@article{osti_1429358,
title = {Accurate Projection Methods for the Incompressible Navier–Stokes Equations},
author = {Brown, David L. and Cortez, Ricardo and Minion, Michael L.},
abstractNote = {This paper considers the accuracy of projection method approximations to the initial–boundaryvalue 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 secondorder methodology a decade and a half ago. It has been observed that while the velocity can be reliably computed to secondorder accuracy in time and space, the pressure is typically only firstorder accurate in the L∞norm. Here, we identify the source of this problem in the interplay of the global pressureupdate formula with the numerical boundary conditions and presents an improved projection algorithm which is fully secondorder 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 secondorder 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.},
doi = {10.1006/jcph.2001.6715},
journal = {Journal of Computational Physics},
number = 2,
volume = 168,
place = {United States},
year = {2001},
month = {4}
}
Web of Science
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