香农透计算在纳维埃-斯托克斯流量问题使用随机有限体积方法
Marcin Kamiński1, Rafał Leszek Ossowski1
1Faculty of Civil Engineering, Architecture and Environmental Engineering, Lodz University of Technology, 90-924 Łódź, Poland.
Entropy (Basel, Switzerland)
|January 24, 2025
概括
本研究提出了一种新的随机有限体积方法 (SFVM),用于解决具有不确定性的流体流程方程. 该方法准确地模拟了概率流体动力学,包括热传导和盖子驱动的腔流.
科学领域:
- 计算流体动力学的流体动力学.
- 数字分析 数字分析
- 流体力学 流体力学 流体力学
背景情况:
- 纳维埃-斯托克斯方程控制流体的流动.
- 将物理不确定性纳入流体动力学是非常重要的.
- 需要随机方法来处理这些不确定性.
研究的目的:
- 开发和实施一个更高阶的随机有限体积方法 (SFVM) 解决不可压缩,非流和低音流体流与高斯不确定性.
- 分析流体流动的概率方面,包括压力-速度-温度 (PVT) 解决方案.
- 扩展SFVM用于模拟具有不确定性的复杂流体动力学问题.
主要方法:
- 使用了高阶随机有限体积方法 (SFVM) 与代通用随机扰动和蒙特卡洛方案相结合.
- 在PVT解决方案中使用多项式基础和加权最小平方法 (WLSM).
- 解决了使用OpenFVM的确定性问题,使用MAPLE 2019用于LSM配件,以及用于可视化的FEPlot.
主要成果:
- 成功计算了概率量,包括前两个概率时刻和香农的空间分布.
- 使用2D传热基准测试验证实了该方法.
- 将该方法应用于概率的3D合盖驱动腔流分析和2D盖驱动腔流,粘度和导热率不确定.
结论:
- 开发的SFVM为分析具有物理不确定性的流体流提供了一个强大的框架.
- 该方法证明了对复杂问题的准确性和适用性,例如盖子驱动的腔流.
- 未来的扩展包括整合人工神经网络以适应基础近似.
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