Development of highly accurate interpolation methodfor mesh‐free flow simulations III. Analysis of accuracy and stability

Abstract

AbstractA 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.