Adjoint-based particle forcing reconstruction from sparse measurements with uncertainty quantification

The drag law of particles within turbulent environments influences dynamical properties pertinent to many applications such as the mining industry or supersonic aerodynamics. The current study explores the determination of the forcing function for one-way coupled passive particles, under the assumption that the ambient velocity fields are known. When measurements regarding particle locations are available but sparse, direct evaluation of the forcing is intractable. Nevertheless, the forcing for finite-size particles is determined using adjoint-based data assimilation. This inverse problem is formulated within the framework of optimization, where the cost function is defined as the difference between the measured and predicted particle locations. The gradient of the cost function, with respect to the forcing, can be calculated from the coupling between the forward and adjoint particle traces. When measurements are subject to Gaussian noise, samples within the posterior probability distribution of the forcing function can be drawn using Hamiltonian Monte Carlo (HMC). The algorithm is tested in both the elementary Arnold–Beltrami–Childress (ABC) flow and homogeneous isotropic turbulence.