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Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion: Two-Dimensional Incompressible Flow. Part I

✍ Scribed by Akio Arakawa

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 372 KB
Volume: 135
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1997.5697

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✦ Synopsis

The integral constraints on quadratic quantities of physical importance, such as conservation of mean kinetic energy and mean square vorticity, will not be maintained in finite difference analogues of or the equation of motion for two-dimensional incompressible flow, unless the finite difference Jacobian expression for the advection term is restricted to a form which properly represents the interaction

between grid points, as derived in this paper. It is shown that the derived form of the finite difference Jacobian prevents nonlinear computational instability and thereby permits long-term numerical where J is the Jacobian operator with respect to the rectanintegrations.

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