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A little more on stabilized Q 1 Q 1 for transient viscous incompressible flow
Author(s) -
Gresho P. M.,
Chan S. T.,
Christon M. A.,
Hindmarsh A. C.
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650211005
Subject(s) - projection (relational algebra) , flow (mathematics) , simple (philosophy) , divergence (linguistics) , incompressible flow , euler's formula , mathematics , transient (computer programming) , compressibility , projection method , computational fluid dynamics , physics , algorithm , mathematical analysis , computer science , geometry , mechanics , dykstra's projection algorithm , philosophy , linguistics , epistemology , operating system
In an attempt to overcome some of the well‐known ‘problems’ with the Q 1 P 0 element, we have devised two ‘stabilized’ versions of the Q 1 Q 1 element, one based on a semi‐implicit approximate projection method and the other based on a simple forward Euler technique. While neither one conserves mass in the most desirable manner, both generate a velocity field that is usually ‘close enough’ to divergence‐free. After attempting to analyse the two algorithms, each of which includes some ad hoc ‘enhancements’, we present some numerical results to show that they both seem to work well enough. Finally, we point out that any projection method that uses a ‘pressure correction’ approach is inherently limited to time‐accurate simulations and, even if treated fully implicitly, is inappropriate for seeking steady states via large time steps.