動径基底函数を用いた球面上のセミ・ラグランジュ移流

Abstract

Radial basis functions (RBF) have been used to construct an interpolant from scattered nodes, such as quasi-uniform nodes on the sphere. The RBF advective operator was shown to be well posed on the sphere and an Eulerian advection model on the sphere was constructed in the literature. In the present study, the advection operator is replaced with the upstream trajectory calculation and RBF interpolation to construct a semi-Lagrangian model on the sphere. The semi-Lagrangian model is found to be more accurate than the Eulerian model in the advection of cosine bell and to have much smaller ripples away from the bell. The semi-Lagrangian model presented in this study is a promising approach because of better accuracy and a longer time step than the Eulerian model.