2204 正二十面体球面格子におけるCIP/Multi-Moment有限体積法について(S01-1 CIP法の新展開と保存形(1),S01 CIP法の新展開と保存形)

抄録

We propose a high-order finite volume method based on multi-moment, namely constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM), on the icosahedral spherical grid. In this method, two kinds of moments are defined as model variables on physical field, for example the point value (PV) and the volume-integrated average (VIA), and updated independently in time. Therefore, a CIP/MM FVM appears to be more attractive regarding the stability and flexibility in comparison with other conventional single-moment finite volume methods that use only the VIA as the model variable. The icosahedral spherical grid has a significant advantage of grid uniformity. We have developed a CIP/MM FVM formulations for the advection equation and the shallow-water equations on the sphere, and carried out some numerical experiments to varify the numerical schemes.