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.

CFD-MRI: A coupled measurement and simulation approach for accurate fluid flow characterisation and domain identification

“…This is based on the idea of Pingen et al [22] , who used a porosity function to scale the velocity in the equilibrium distribution function, which recovers the Brinkman equations for flow through porous media. The porous media BGK Boltzmann equation introduced by Krause et al [4,5] is defined as…”

“…The main aim of this manuscript is to introduce, realise and validate the proposed CFD-MRI method for the coupling of measured data and simulation using the adjoint lattice Boltzmann method (ALBM) for solving fluid flow domain identification problems [4,5] . The method is used to locate an object and the flow field using only limited 2 D spatially resolved MRI data with one velocity component.…”

“…The first to use LBM for topology optimisation were Pingen et al [22] using a porous media model. Based on this, Krause et al [4,5] have proposed an extension to the ALBM for the determination of flow areas and flow dynamics. Thereby, porosity is the control variable of an optimisation problem that minimises the resulting velocity distributions to those of a measured one.…”

“…The ALBM was validated for domain identification problems for different and increasingly complex objects and with complete and partially available artificial data (cf. [4,5] ). However, no validation of the algorithm with measurement data was performed, which is one of the formulated aims of this manuscript.…”

Reactive fluid flow topology optimization with the multi-relaxation time lattice Boltzmann method and a level-set function

“…Since the pioneering work of Pingen [25], adjoint-state LBM methods have also been developed for uid ow identication [26,27] or topology optimization [15,28,29]. It is also to be noticed that the LBM computational time of both forward and adjoint-state problems can be signicantly reduced with GPU parallel computing [3032].…”