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Calculation of laminar flows with second‐order schemes and collocated variable arrangement
Author(s) -
Biagioli Fernando
Publication year - 1998
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(19980430)26:8<887::aid-fld670>3.0.co;2-o
Subject(s) - upwind scheme , mathematics , discretization , laminar flow , extrapolation , total variation diminishing , richardson extrapolation , flux limiter , mathematical analysis , geometry , mechanics , physics
A numerical study of laminar flows is carried out to examine the performance of two second‐order discretization schemes: a total variation diminishing scheme and a second‐order upwind scheme. The former has the same form as the standard first‐order hybrid central upwind scheme, but with a numerical diffusion reduced by the Van Leer limiter; the latter is based on the linear extrapolation of cell face values using the two upwind neighbors. A collocated grid arrangement is used; oscillations which could be generated by pressure–velocity decoupling are avoided via the Rhie–Chow interpolation. Two iterative solution methods are used: (i) the deferred correction procedure proposed by Khosla and Rubin and (ii) implicit treatment of the second‐order upwind contribution. Three two‐dimensional laminar test cases are considered for assessment: the plane lid‐driven cavity, the plane backward facing step and the axisymmetric pipe with sudden contraction. Experimental data are available for the two last cases. Both the total variation diminishing and the second‐order upwind schemes give wiggle‐free results and can predict the flowfields more accurately than the standard first‐order hybrid central upwind scheme. © 1998 John Wiley & Sons, Ltd.