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Development of highly accurate interpolation methodfor mesh‐free flow simulations III. Analysis of accuracy and stability
Author(s) -
Tanaka Nobuatsu
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.461
Subject(s) - stability (learning theory) , interpolation (computer graphics) , mathematics , curvature , scalar (mathematics) , advection , computation , taylor series , mathematical analysis , algorithm , computer science , geometry , physics , classical mechanics , motion (physics) , machine learning , thermodynamics
A highly accurate interpolation method, CIVA, improves the accuracy of mesh‐free and grid‐less methods by taking into consideration first‐order spatial derivatives as variables; an approach based on the same idea as that on which CIP is based. In this study, the accuracy and stability of CIVA is evaluated by analytically and numerically. First, the general formulation of CIVA for the n ‐dimensional case is described. Since CIVA contains the bubble function, we consider the determination methods: constant curvature condition and utilization of another computing point. Then, the relation between the bubble function in the CIVA method and the accuracy and stability is made clear by the analysis based on the Taylor expansion. Some computations of two‐dimensional passive scalar advection and advection–diffusion problems are performed for the verification of accuracy and stability. Copyright © 2003 John Wiley & Sons, Ltd.