A flexible framework for shape optimisation is presented for incompressible Newtonian fluids using lattice Boltzmann methods. It is proposed to solve optimisation problems using line search methods, with design sensitivities obtained through forward propagation automatic differentiation. The underlying fluid flow problems are modelled by homogenised lattice Boltzmann methods, wherein permeability is varied to propagate derivative information at parametrised boundaries. The parametrisation is realised by describing the geometry using smooth indicator functions that have analytically differentiable boundaries. A number of simulation results are presented using the open-source software OpenLB (Krause et al., 2017), validating the approach and evaluating its application to domain identification and drag minimisation.

提出了使用格子Boltzmann方法对不可压缩牛顿流体进行形状优化的灵活框架。提出使用线搜索方法解决优化问题，并通过前向传播自动微分获得设计灵敏度。潜在的流体流动问题通过均质化的格子Boltzmann方法建模，其中渗透率发生变化以在参数化边界处传播导数信息。通过使用具有解析可区分边界的平滑指示符功能描述几何形状，可以实现参数设置。使用开源软件OpenLB（Krause et al。，2017）提出了许多仿真结果，验证了该方法并评估了其在域识别和阻力最小化方面的应用。