<span style="white-space: normal;">可压缩Navier-Stokes方程的时空耦合优化低维动力系统建模方法</span>

齐进; 吴锤结

doi:10.21656/1000-0887.430220

Volume 43 Issue 10

Oct. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(10): 1053-1085

齐进, 吴锤结. 可压缩Navier-Stokes方程的时空耦合优化低维动力系统建模方法[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1053-1085. doi: 10.21656/1000-0887.430220

Citation:

齐进, 吴锤结. 可压缩Navier-Stokes方程的时空耦合优化低维动力系统建模方法[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1053-1085. doi: 10.21656/1000-0887.430220

Citation:

齐进, 吴锤结. 可压缩Navier-Stokes方程的时空耦合优化低维动力系统建模方法[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1053-1085. doi: 10.21656/1000-0887.430220

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可压缩Navier-Stokes方程的时空耦合优化低维动力系统建模方法

doi: 10.21656/1000-0887.430220

齐进^1
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吴锤结^{2
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1.
北京应用物理与计算数学研究所，北京 100088
2.
大连理工大学航空航天学院，辽宁大连 116024

Received Date: 2022-07-01
Rev Recd Date: 2022-09-30

Available Online: 2022-10-20

Publish Date: 2022-10-31

Abstract

Abstract

当采用低维动力系统模型研究Navier-Stokes方程的动力学性质时，保持低维模型的吸引域与Navier-Stokes方程的吸引域相同是非常重要的。然而，到目前为止，还没有一种普适的方法能确保对于一般问题都能达到这一目的。该文发现任何基于空间基的低维模型，如本征正交分解基、优化空间基和其他经典空间基，都不具有可预测性，即低维动力系统的误差随着流场的时间演化而增大。在构造优化动力系统的理论框架和时空耦合谱展开的新概念下，该文构造了可压缩Navier-Stokes方程的低维模型来逼近大涡模拟方程的数值解，给出了高精度的流场数值模拟结果和全新的时空耦合基时空演化数值结果。全场误差在10⁻²%以下，而每个网格点的平均误差在10⁻⁸%以下。时空耦合化化低维动力系统可以保证低维模型的吸引域与Navier-Stokes方程的吸引域相同。因此，保证了时空耦合优化低维动力系统的特征动力学性质与真实流场的特征动力学性质是一致的。
- 时空耦合谱展开,
- 时空耦合优化低维动力系统,
- 可压缩Navier-Stokes方程,
- 大涡模拟,
- 大涡模拟

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References(41)

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