一维浅水磁流体力学方程在拉格朗日坐标下的不变守恒有限差分格式
数值分析
2024-02-28 v7 数值分析
摘要
针对具有磁场且不同底部地形的一维浅水方程,构造了不变有限差分格式。基于作者近期完成的群分类结果,获得了原微分模型守恒律的有限差分类比。数值考察了若干典型问题,并对有磁场情形与无磁场情形(标准浅水模型)进行了比较。还讨论了拉格朗日坐标下差分格式的不变性以及所得数值解的能量保持性质。
引用
@article{arxiv.2304.03488,
title = {Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates},
author = {E. I. Kaptsov and V. A. Dorodnitsyn},
journal= {arXiv preprint arXiv:2304.03488},
year = {2024}
}
备注
22 pages, 6 figures. This version (v7) has been specially prepared for publication in the Open Commun. Nonlinear Math. Phys., Special Issue in Memory of Professor Decio Levi. Notice that in the previous version (v5) of the paper an appendix was added with an informal discussion on stability issues. By the decision of the authors, this appendix was not included in v6 and v7