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The third‐order polynomial method for two‐dimensional convection and diffusion
Author(s) -
Tkalich Pavlo,
Chan Eng Soon
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.483
Subject(s) - polynomial , mathematics , term (time) , convection–diffusion equation , computation , diffusion , numerical diffusion , stability (learning theory) , series (stratigraphy) , numerical stability , scheme (mathematics) , upwind scheme , node (physics) , numerical analysis , mathematical analysis , algorithm , computer science , mechanics , physics , biology , thermodynamics , discretization , paleontology , quantum mechanics , machine learning
Using the upstream polynomial approximation a series of accurate two‐dimensional explicit numerical schemes is developed for the solution of the convection–diffusion equation. A third‐order polynomial approximation (TOP) of the convection term and a consistent second‐order approximation of the diffusion term are combined in a single‐step flux‐difference algorithm. Stability analysis confirms that the TOP‐12 scheme satisfies the CFL condition for two dimensions. Using smaller and narrower flux stencils compared to algorithms of similar accuracy, the TOP‐12 scheme is more efficient in terms of computations per single node. Numerical tests and comparison with other well‐known algorithms show a high performance of the developed schemes. Copyright © 2003 John Wiley & Sons, Ltd.