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

This article presents the coupling of magnetic resonance imaging (MRI) measurements and computational fluid dynamics (CFD) for accurate characterisation of fluid flow and identification of flow domains. Currently, MRI measurements are averaged over time and space, assuming a certain smoothness of the velocity and pressure space. However, a possible solution of a fluid problem must fulfil the Navier-Stokes equations, which sets up a condition that is much more restrictive than the usual smoothness assumptions in e.g. curve fitting. The novel CFD-MRI method uses this insight to reduce the statistical noise and to identify finer structures of the underlying domain. The problem is formulated as a distributed control problem which minimises the distance between measured and simulated flow field. Thereby, the simulated flow field is the solution of a parametrised porous media BGK-Boltzmann equation which approaches a homogenised Navier-Stokes equation in the hydrodynamic limit. The parameters represent the porosity distributed in the domain which yields a domain and a fluid flow that fits best to the measured data. This enables the method they locate an obstacle and the flow field from limited 2D spatially resolved MRI data with one velocity component. The problem is solved with an adjoint lattice Boltzmann method (ALBM) using the open source software OpenLB1.