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An analysis and comparison of the time accuracy of fractional‐step methods for the Navier–Stokes equations on staggered grids
Author(s) -
Armfield S.,
Street R.
Publication year - 2002
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.217
Subject(s) - momentum (technical analysis) , convergence (economics) , navier–stokes equations , coupling (piping) , iterated function , mathematics , projection (relational algebra) , boundary value problem , iterative method , projection method , mathematical analysis , boundary (topology) , physics , mechanics , mathematical optimization , algorithm , dykstra's projection algorithm , compressibility , mechanical engineering , finance , engineering , economics , economic growth
Fractional‐step methods solve the unsteady Navier–Stokes equations in a segregated manner, and can be implemented with only a single solution of the momentum/pressure equations being obtained at each time step, or with the momentum/pressure system being iterated until a convergence criterion is attained.The time accuracy of such methods can be determined by the accuracy of the momentum/pressure coupling, irrespective of the accuracy to which the momentum equations are solved. It is shown that the time accuracy of the basic projection method is first‐order as a result of the momentum/pressure coupling, but that by modifying the coupling directly, or by modifying the intermediate velocity boundary conditions, it is possible to recover second‐order behaviour. It is also shown that pressure correction methods, implemented in non‐iterative or iterative form and without special boundary conditions, are second‐order in time, and that a form of the non‐iterative pressure correction method is the most efficient for the problems considered. Copyright © 2002 John Wiley & Sons, Ltd.