Solving fluid flow domain identification problems with adjoint lattice Boltzmann methods

Abstract

In this article, the adjoint lattice Boltzmann method (ALBM) for solving fluid domain identification problems for incompressible fluids, proposed by Krause et al. (2016), is improved and validated. The problem is formulated as a distributed control problem which minimises the distance between a given, e.g. from measurements like MRI, and a simulated flow field. Thereby, the simulated flow field is the solution of a parametrised porous media BGK–Boltzmann problem, where the parameters represent porosity distributed in the domain. The proposed parametrisation consists of linking the variables representing a lattice-dependent porosity with the control variables. Hereby, it is paid attention that a given control parameter set yields results which are independent of the underlying grid resolution. It enables solving an optimisation problem with different resolutions without adapting the initial set of control variables.