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Pressure Stability in Fractional Step Finite Element Methods for Incompressible Flows

✍ Scribed by Ramon Codina

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
509 KB
Volume
170
Category
Article
ISSN
0021-9991

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✦ Synopsis

The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure Poisson equation. For the classical first-order projection method, it is shown that there is a pressure control which depends on the time step size, and therefore there is a lower bound for this time step for stability reasons. The situation is much worse for a second-order scheme in which part of the pressure gradient is kept in the momentum equation. The pressure stability in this case is extremely weak. To overcome these shortcomings, a stabilized fractional step finite element method is also considered, and its stability is analyzed. Some simple numerical examples are presented to support the theoretical results.

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