Shape Optimization Using the Adjoint Lattice Boltzmann Method for Aerodynamic Applications

The present work focuses on shape optimization using the lattice Boltzmann method applied to aerodynamic cases. The adjoint method is used to calculate the sensitivities of the drag force with respect to the shape of an object. The main advantage of the adjoint method is its cost, because it is independent from the number of optimization parameters. The approach used consists in developing a continuous adjoint of the primal problem discretized in space, time, and velocities. An adjoint lattice Boltzmann equation is thus found, which is solved using the same algorithms as in the primal problem. The test cases investigate new features compared to what exists in the literature, such as the derivation of the grid refinement models in the primal problem to obtain their adjoint counterparts, but also the derivation of a double-relaxation-time algorithm and the Ginzburg et al. interpolation at the wall ("Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure and Mixed Boundary Conditions," Communications in Computational Physics, Vol. 3, No. 2, 2008, pp. 427-478). Regarding the unsteadiness of the primal problem, two methods differing in accuracy and computational effort are compared using a two-dimensional unsteady case. Finally, this first-of-a-kind adjoint solver is applied to a large-scale threedimensional turbulent case (the flow of air around a car at a speed of 130 km/h), which shows its usefulness in the industry.