A framework for simultaneous aerodynamic design optimization in the presence of chaos
A framework for simultaneous aerodynamic design optimization in the presence of chaos
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DOI：
10.1016/j.jcp.2016.10.043
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Stefanie Günther;N. Gauger;Qiqi Wang
中科院分区：
文献类型：
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作者：
Stefanie Günther;N. Gauger;Qiqi Wang
由于经典时间步长方法的时间前向信息传播，将现有的非定常偏微分方程组的求解器整合到一种同时优化方法中是具有挑战性的。本文将同时单步单次最优化方法应用于重新定义的非定常约束，该约束同时允许信息在时间上向前传播和向后传播。特别是在存在混沌和湍流的情况下，同时求解初值问题和优化问题往往不能很好地随时间域长度的变化而变化。新公式放宽了初始条件，代之以求解离散偏微分方程组的最小二乘问题。这实现了与时间域长度无关的高效单次优化，即使在存在混沌的情况下也是如此。
Integrating existing solvers for unsteady partial differential equations into a simultaneous optimization method is challenging due to the forward-in-time information propagation of classical time-stepping methods. This paper applies the simultaneous single-step one-shot optimization method to a reformulated unsteady constraint that allows for both forward- and backward-in-time information propagation. Especially in the presence of chaotic and turbulent flow, solving the initial value problem simultaneously with the optimization problem often scales poorly with the time domain length. The new formulation relaxes the initial condition and instead solves a least squares problem for the discrete partial differential equations. This enables efficient one-shot optimization that is independent of the time domain length, even in the presence of chaos.