论文标题
基于三维stokes液滴的基于伴随的控制
Adjoint-based Control of Three Dimensional Stokes Droplets
论文作者
论文摘要
我们开发了一个连续的伴随公式和实现，以控制斯托克斯中清洁，中性浮力的液滴的变形，流过Farfield速度边界条件。重点是动态，表面张力通过年轻的宽面法发挥了重要作用。要执行优化，我们需要访问一阶梯度信息，我们通过将形状计算将其应用于接口演化形成的时空管，从线性化的灵敏度方程及其相应的伴随中获得。我们表明，可以通过标量横向场有效地表达伴随演化方程。最佳控制问题通过使用正交的高阶边界积分方法通过扩展与液滴表面几何形状的球形谐波表示相结合而离散。我们在几个跟踪型控制问题上显示了该方案的准确性和稳定性。
We develop a continuous adjoint formulation and implementation for controlling the deformation of clean, neutrally buoyant droplets in Stokes flow through farfield velocity boundary conditions. The focus is on dynamics where surface tension plays an important role through the Young-Laplace law. To perform the optimization, we require access to first-order gradient information, which we obtain from the linearized sensitivity equations and their corresponding adjoint by applying shape calculus to the space-time tube formed by the interface evolution. We show that the adjoint evolution equation can be efficiently expressed through a scalar adjoint transverse field. The optimal control problem is discretized by high-order boundary integral methods using Quadrature by Expansion coupled with a spherical harmonic representation of the droplet surface geometry. We show the accuracy and stability of the scheme on several tracking-type control problems.
