14:15 〜 14:30
[AAS05-03] Preliminary validation of the applicability of the multigrid method to multi-scale representation of fluids
キーワード：マルチグリッド法、マルチスケールモデル、浅水波方程式
Multiscale models perform calculations using multiple lengths and time scales to represent hierarchical structures in the atmosphere and ocean. They can be broadly classified into two methods: systematic asymptotics and superparameterization (Grooms & Julien, 2018). On the other hand, the multigrid method is a method that efficiently reduces errors by proceeding with calculations while changing the grid size and is a beneficial computational method, especially for elliptic boundary value problems (Trottenberg, 2007). In this study, the shallow water wave equation was solved using the multigrid method as a first step to verify the possibility of multiscale representation using the multigrid method. The correspondence between each layer of the multigrid method and the multiscale representation was verified. The results showed that for the semi-implicit discretization method used in this study, the values at each layer are linear interpolations of the values at the finest layer when the multigrid method is applied as is. The results also showed that the appearance of the solution differs depending on the time interval, suggesting the need to introduce multiple length scales in the time direction.