An adjoint-based lattice Boltzmann method for noise control problems

In this paper optimal control of acoustic problems is addressed within the lattice Boltzmann method framework. To this end, an adjoint-based lattice Boltzmann method is proposed to solve the adjoint problem. The adjoint state provides an easy access to the optimization gradients. The line search step in Newton's descent method is performed through a combination of complex differentiation and adjoint problem in the lattice Boltzmann method. The implementation of an active noise reduction method for two-dimensional weakly compressible (low Mach number) flows is discussed, and the applicability of the method is assessed.