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Accurate multi‐level schemes for advection
Author(s) -
Kim Cheolwan
Publication year - 2003
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.443
Subject(s) - advection , stencil , upwind scheme , mathematics , dissipative system , flow (mathematics) , computational fluid dynamics , phase space , computer science , mathematical analysis , mechanics , geometry , physics , discretization , computational science , quantum mechanics , thermodynamics
The upwind leapfrog method for the advection equation, which is non‐dissipative and very accurate, is extended to higher‐order and multiple dimensions. The higher‐order version is developed by extending the stencil into space and time, and an analysis of the phase error is given. The schemes are then successfully applied to the classical test cases of rotating flow, and to a more realistic problem of non‐uniform advection. Copyright © 2003 John Wiley & Sons, Ltd.