On Discrete Projection and Numerical Boundary Conditions for the Numerical Solution of the Unsteady Incompressible Navier-Stokes Equations
Year: 2002
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 1 : pp. 35–56
Abstract
The unsteady incompressible Navier-Stokes equations are discretized in space and studied on the fixed mesh as a system of differential algebraic equations. With discrete projection defined, the local errors of Crank Nicholson schemes with three projection methods are derived in a straightforward manner. Then the approximate factorization of relevant matrices are used to study the time accuracy with more detail, especially at points adjacent to the boundary. The effects of numerical boundary conditions for the auxiliary velocity and the discrete pressure Poisson equation on the time accuracy are also investigated. Results of numerical experiments with an analytic example confirm the conclusions of our analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2002-JCM-8897
Journal of Computational Mathematics, Vol. 20 (2002), Iss. 1 : pp. 35–56
Published online: 2002-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Differential algebraic equations Discrete projection Numerical boundary conditions.