Global, nonparametric, noniterative optimization of time-averaged quantities under small, time-varying forcing: An application to a thermal convection field
Global, nonparametric, noniterative optimization of time-averaged quantities under small, time-varying forcing: An application to a thermal convection field
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DOI：
10.1080/10407790.2019.1665436
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发表时间：
2019-10-03
影响因子：
1
通讯作者：
Kawahara，Genta
中科院分区：
文献类型：
--
作者：
Ishida，Hideshi;Ihara，Shiho;Kawahara，Genta
本研究证明了一类受时变强迫振动的指数的时间均值的全局、非参数、非迭代优化。它是基于非自治常微分方程组的(定常)强迫振动可以用解析解很好地逼近的事实，当强迫的幅值足够小，并且其无强迫的基态是线性稳定和稳定的。将其应用于具有水平温差的方腔内二维热对流场的时间平均换热系数的优化，首次得到了振动强迫的全局最优方式，即振动热源和涡量源的全局最优空间分布。最大振动热对流与重力内波共振状态很好地对应。相反，最小化的热对流很弱，使两侧的边界层保持较厚。
This study demonstrates a global, nonparametric, noniterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of nonautonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.