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Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations
Author(s) -
Pascau A.
Publication year - 2011
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.2215
Subject(s) - decoupling (probability) , interpolation (computer graphics) , computational fluid dynamics , mathematics , face (sociological concept) , simple (philosophy) , computer science , calculus (dental) , mechanics , physics , motion (physics) , engineering , medicine , social science , dentistry , control engineering , artificial intelligence , sociology , philosophy , epistemology
Abstract The use of a colocated variable arrangement for the numerical solution of fluid flow is becoming more and more popular due to its coding simplicity. The inherent decoupling of the pressure and velocity fields in this arrangement can be handled via a special interpolation procedure for the calculation of the cell face velocity named pressure‐weighted interpolation method (PWIM) ( AIAA J. 1983; 21 (11):1525–1532). In this paper a discussion on the alternatives to extend PWIM to unsteady flows is presented along with a very simple criterion to ascertain if a given interpolation practice will produce steady results that are relaxation dependent or time step dependent. Following this criterion it will be shown that some prior schemes presented as time step independent are actually not, although by using special interpolations can be readily adapted to be. A systematic way of deriving different cell face velocity expressions will be presented and new formulae free of Δ t dependence will be derived. Several computational exercises will accompany the theoretical discussion to support our claims. Copyright © 2009 John Wiley & Sons, Ltd.