Development of self-adaptive moving mesh methods for numerical computations of phenomena with large deformation based on the theory of integrable systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04909
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Waseda University
• Principal Investigator: Maruno Kenichi 早稲田大学, 理工学術院, 教授 (80380674)
• Co-Investigator(Kenkyū-buntansha): 太田 泰広 神戸大学, 理学研究科, 教授 (10213745) ; 高橋 大輔 早稲田大学, 理工学術院, 教授 (50188025)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 自己適合移動格子スキーム / 非線形波動 / 可積分離散化 / 構造保存型差分スキーム / 離散微分幾何学

Outline of Final Research Achievements

We developed the theory of integrable discretization of nonlinear wave equations and self-adaptive moving mesh schemes. We constructed discrete analogues of coupled short pulse equation, coupled Yajima-Oikawa system, reduced Ostrovsky equation, modified short pulse equation, Degasperis-Procesi equation based on the theory of integrable systems. We also studied accuracy of numerical computations of our self-adaptive moving mesh scheme of the modified short pulse equation which has cusped soliton solutions. We also studied numerical schemes of a mathematical model of one-dimensional soil water infiltration using self-adaptive moving mesh schemes and we verified its numerical accuracy. We also investigated the relationship between self-adaptive moving mesh schemes and discrete differential geometry.

Free Research Field

応用数学，非線形波動，応用可積分系，数理物理、数値計算法