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IMPOSING ‘NO’ BOUNDARY CONDITION AT OUTFLOW: WHY DOES IT WORK?
Author(s) -
Renardy Michael
Publication year - 1997
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/(sici)1097-0363(19970228)24:4<413::aid-fld507>3.0.co;2-n
Subject(s) - boundary value problem , boundary (topology) , outflow , mixed boundary condition , free boundary problem , mathematics , work (physics) , no slip condition , robin boundary condition , neumann boundary condition , boundary conditions in cfd , partial differential equation , mathematical analysis , underdetermined system , singular boundary method , geometry , physics , boundary element method , finite element method , meteorology , thermodynamics
In recent work on outflow boundary conditions for Navier–Stokes equations by Papanastasiou et al. ( Int. j. numer. methods fluids , 14 , 587–608 (1992)) a choice has been proposed which can formally be described as imposing no boundary condition at all. This of course leads to an underdetermined problem at the level of the partial differential equations. However, it yields a well‐defined problem at the discrete level and it has been documented that this choice of outflow conditions performs in a way which is superior to more ‘standard’ artificial boundary conditions. In this paper we analyse a one‐dimensional model problem. We shall show that the ‘free’ boundary condition of Papanastasiou et al. actually imposes an effective boundary condition. This effective boundary condition is identified and its advantages are discussed. © 1997 by John Wiley and Sons, Ltd.