Adjoint Lattice Boltzmann for topology optimization on multi-GPU architecture

In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint formulation is used to calculate sensitivity of the LBM solution to several type of parameters, both global and local. The numerical scheme for solving the adjoint problem has many properties of the original system, including locality and explicit time-stepping. Thus it is possible to integrate it with the standard LBM solver, allowing for straightforward and efficient parallelization (overcoming limitations typical for the discrete adjoint solvers). This approach is successfully used for the channel flow to design a free-topology mixer and a heat exchanger. Both resulting geometries being very complex maximize their objective functions, while keeping viscous losses at acceptable level.