Accurate Projection Methods for the Incompressible Navier-Stokes Equations
(D. Brown, R. Cortez and M. Minion)

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-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 an impulse formulation of the incompressible Navier-Stokes equations is discussed, which provides another option for obtaining fully second-order convergence in both velocity and pressure. The connection between the boundary conditions for projection methods and impulse methods is explained in detail.

J. Comput. Phys., 168, (2001) pp. 464-499.

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LaTeX Bibliography:

@article{BrownCortezMinion2001,
        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.},
        volume = {168},
        number = {2},
        month = {Apr.},
        year = {2001},
        pages = {464--499}
}

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