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Convective difference schemes and Hermite interpolation
Author(s) -
Fischer Karsten
Publication year - 1978
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620120605
Subject(s) - interpolation (computer graphics) , mathematics , hermite interpolation , stability (learning theory) , context (archaeology) , hermite polynomials , variable (mathematics) , numerical analysis , reduction (mathematics) , work (physics) , convection , series (stratigraphy) , mathematical analysis , computer science , geometry , mechanics , physics , animation , paleontology , computer graphics (images) , machine learning , biology , thermodynamics
A new method for numerically solving the convection equation is presented. The reduction of numerical errors is achieved by introducing an auxiliary variable and solving an auxiliary equation for the latter. The method is based on a Hermite interpolation of the convected quantity. Three explicit numerical versions of the method are investigated and compared with some of the most widely used schemes, and it is shown that the new method gives better physical results. Arguments are given that the usual mathematical series expansions do not work sufficiently well in that context. Instead of using linear stability analyses the quality of the method is investigated by numerical experiments.