We present the usage of an adjoint Lattice Boltzmann Method (LBM) for open-loop control of two-dimensional flapping wing motion. Movement of the wing is parametrised with periodic B-Splines, while the wing interacts with the surrounding flow via an Immersed Boundary (IB) method. Multi-objective optimisation is performed using a gradient optimisation algorithm, for which sensitivities are calculated with an adjoint method. The objectives selected were the mean lift force and mechanical power. To achieve performance suitable for optimisation, we also present an efficient GPU implementation of the LBM and adjoint LBM. The Immersed Boundary approach employed for the LBM is verified against results from the literature, while for the flapping case it is compared with two different Finite Volume Method (FVM) approaches. The obtained Pareto front of optimal designs shows a clear discrepancy between the power consumption and the mean lift force. A significant improvement of the basic wing design is demonstrated, and highlights the applicability of adjoint LBM simulations in complex open-loop control problems.

我们提出了使用伴随格子Boltzmann方法（LBM）的二维扑翼运动的开环控制。机翼的运动通过周期性B样条曲线进行参数设置，而机翼则通过浸入边界（IB）方法与周围的水流相互作用。使用梯度优化算法执行多目标优化，为此使用伴随方法计算灵敏度。选择的目标是平均升力和机械功率。为了获得适合优化的性能，我们还介绍了LBM和伴随LBM的高效GPU实现。针对LBM的浸入边界方法已针对文献结果进行了验证，而对于拍打情况，则将其与两种不同的有限体积方法（FVM）方法进行了比较。所获得的最佳设计的帕累托前沿显示出功率消耗和平均举升力之间存在明显差异。演示了基本机翼设计的重大改进，并强调了伴随LBM模拟在复杂开环控制问题中的适用性。