Geometry reconstruction from magnetic resonance velocimetry measurements via solving an inverse fluid flow problem

Computational fluid dynamics (CFD) simulations are an essential method for addressing complex physical flow problems, e.g., heterogeneous reactive flows through open cell foams (OCF) with catalytic coating. To conduct numerical studies in such intricate flow domains, expensive methods such as computer tomography (CT) scans might be necessary to acquire the morphological model. The current work explores an alternative approach to obtain the flow domain from given or measured velocity distributions, where the latter are acquired through magnetic resonance velocimetry (MRV). An inverse Navier–Stokes problem is solved by a numerical framework implemented in the open source library OpenLB, combining the adjoint homogenized lattice Boltzmann method and the quasi-Newton method LBFGS. Therein, the deviation between the measured and simulated velocity distributions is the target of the minimization problem by iteratively adjusting the permeability distribution in the flow, representing the reconstructed topology model. Comprehensive numerical experiments investigate the impact of different aspects, e.g., numerical grid resolution, Reynolds number, and amplitude of artificial noise signals on the input velocity data, on the inverse problem. First, simulated velocity distributions using a CT-scan model of the OCF and then measured MRV data are used as the input for the inverse problem. In the latter, the reconstructed topology is compared against the CT-scan model. We demonstrated that a complex geometry such as the OCF can be reconstructed from velocity distributions (Jaccard index of 0.91) and identified optimal parameter regimes for the framework to operate. Finally, for the case where measured input data was used we archived an improvement of 12% regarding the recovered geometry over the geometry obtained from the signal amplitude image from magnetic resonance imaging.