Towards shape optimisation of fluid flows using lattice Boltzmann methods and automatic differentiation

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.

Automated summary

A flexible framework for shape optimisation using lattice Boltzmann methods for incompressible Newtonian fluids is proposed. The method utilizes line search methods for optimization problems and obtains design sensitivities through forward propagation automatic differentiation. The approach models fluid flow problems using homogenised lattice Boltzmann methods with varying permeability to propagate derivative information at parametrised boundaries.