## Accurate Projection Methods for the Incompressible Navier-Stokes Equations (2001)

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Venue: | J. Comput. Phys |

Citations: | 70 - 5 self |

### BibTeX

@ARTICLE{Brown01accurateprojection,

author = {David L. Brown and Ricardo Cortez and Michael L. Minion},

title = {Accurate Projection Methods for the Incompressible Navier-Stokes Equations},

journal = {J. Comput. Phys},

year = {2001},

volume = {168},

pages = {464--499}

}

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### Abstract

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. 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 Key Words: incompressible flow; projection method; boundary conditions