对于纳维埃-斯托克斯反向问题的代方法
Liam O'Connor1,2, Daniel Lecoanet1,2, Evan H Anders3
1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
Physical review. E
|May 17, 2024
概括
直接连接循环 (DAL) 与回顾性纳维埃-斯托克斯问题作斗争. 简单的倒向集成 (SBI) 和准可逆方法 (QRM) 为这些反向问题提供了更准确和更有效的解决方案.
科学领域:
- 计算流体动力学的流体动力学.
- 逆向问题理论 逆向问题理论
- 数字分析 数字分析
背景情况:
- 回溯式反向问题,进化系统的时间向后发展,提出了重大挑战.
- 直接连接循环 (DAL) 是一种常见的方法,但它对确定性纳维埃-斯托克斯反向问题的应用是有限的.
- 对2D纳维埃-斯托克斯回顾性问题的DAL的适用性受到质疑.
研究的目的:
- 为了评估DAL对2D纳维埃-斯托克斯反向问题的有效性.
- 将DAL与其他代方法进行比较:简单的逆向集成 (SBI) 和准可逆方法 (QRM).
- 引入和评估一种新的代SBI方法.
主要方法:
- 实施和测试DAL,SBI和QRM用于追溯反向问题.
- 这些方法应用于1D Korteweg-de Vries-Burgers方程和2D Navier-Stokes方程.
- 对每个方法的准确性和代数进行比较分析.
主要成果:
- 达尔在解决回顾式二维纳维埃-斯托克斯反向问题方面表现出局限性.
- 对于测试的问题,SBI和QRM在准确性和效率方面都超过了DAL.
- 由于其后向整合计划中的额外条款,SBI和QRM取得了卓越的结果.
结论:
- DAL不适合追溯的二维纳维埃-斯托克斯反向问题.
- 代SBI和QRM是解决这些追溯反向问题的更有效和高效的替代方案.
- 在向后集成中包含特定术语显著提高了性能.
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