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An improved second moment method for solution of pure advection problems
Author(s) -
Ghods Abdolreza,
Sobouti Farhad,
ArkaniHamed Jafar
Publication year - 2000
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(20000430)32:8<959::aid-fld995>3.0.co;2-7
Subject(s) - advection , numerical diffusion , moment (physics) , flow (mathematics) , diffusion , mathematics , range (aeronautics) , mechanics , numerical analysis , computational fluid dynamics , grid , mathematical analysis , geometry , physics , classical mechanics , aerospace engineering , engineering , thermodynamics
The second moment numerical method (SMM) of Egan and Mahoney [Numerical modeling of advection and diffusion of urban area source pollutant. Journal of Applied Meteorology 1972; 11 : 312–322] is adapted to solve for the pure advection transport equation in a variety of flow fields. SMM eliminates numerical diffusion by employing a procedure that takes into account the first and second moments of mass distribution in each grid element. For pure translational flow fields, the method is conservative, positive definite and shape‐preserving. In rotational and/or shear flows, the accuracy of SMM is significantly reduced. Two improvements are presented to make the SMM applicable to a wider range of flow problems. It is shown that the improved SMM (ISMM) is less diffusive and more shape‐preserving than the SMM in rotational and/or deformational flows. The ISMM can also be used to solve for a color function in compressible flow fields. The computational efficiency of this method is compared with that of other methods and, for a given accuracy, it is shown that ISMM is a cost‐effective, non‐diffusive and shape‐preserving method. Copyright © 2000 John Wiley & Sons, Ltd.