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对于二维雷利-贝纳德对流的无压长期稳定缩小顺序模型
K Chand1, H Rosenberger1, B Sanderse1
1Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, The Netherlands.
Chaos (Woodbury, N.Y.)
|February 26, 2024
概括
本研究介绍了雷利-贝纳德对流的稳定减少序模型 (ROM). 这种新的方法确保了长时间的稳定性,没有额外的机制,准确模拟各种状态的流体动力学.
科学领域:
- 流体动力学 流体动力学
- 计算物理 计算物理
- 热力学是一种热力学.
背景情况:
- 雷利-贝纳德对流是流体热传递的一个基本模型.
- 减少顺序模型 (ROM) 对于高效模拟复杂的流体现象至关重要.
- 在ROM中实现长期稳定,特别是对于混乱的政权,仍然是一个挑战.
研究的目的:
- 开发一个稳定的正确直角分解 (POD) - 基于加勒金的减少顺序模型 (ROM).
- 模拟两个维的雷利-贝纳德对流在稳定状态,周期和混乱状态.
- 用关键的流体动力学指标验证ROM的稳定性和准确性.
主要方法:
- 采用了一个分级网格全序模型 (FOM) 离散.
- 由此产生的ROM无压力,具有偏斜对称的对流术语,以节能.
- 通过分析纳塞尔特和雷诺兹数和温度概况来评估稳定性.
主要成果:
- 在没有人工稳定的情况下,ROM表现出长时间的稳定性,甚至超出了训练数据.
- 定量指标 (纳塞尔特数,雷诺兹数,温度概况) 汇聚到具有增长模式的FOM值.
- 模拟混乱状态需要大量模式来捕捉基本的低能动态.
结论:
- 拟议的POD-Galerkin ROM为模拟雷利-贝纳德对流提供了一种稳定高效的方法.
- 该方法固有的稳定性简化了模拟,并扩大了适用性.
- 混沌动态的准确表示需要仔细的模式选择来解决微小的结构.
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