2024/08/05 by Alexandros Kontogiannis, Kontogiannis, Alexandros, Richard Hodgkinson +3 · 3 citations
Chemical Engineering · #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Rheology and Fluid Dynamics Studies
paper · doi:10.48550/arxiv.2408.02604
openalex publication_date 2024/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct the flow field and learn the unknown N-S parameters. By incorporating a Carreau shear-thinning viscosity model into the N-S problem, we devise an algorithm that learns the most likely Carreau parameters of a shear-thinning fluid, and estimates their uncertainties, from velocimetry data alone. We then conduct a flow-MRI experiment to obtain velocimetry data of an axisymmetric laminar jet through an idealised medical device (FDA nozzle) for a blood analogue fluid. We show that the algorithm can successfully reconstruct the flow field by learning the most likely Carreau parameters, and that the learned parameters are in very good agreement with rheometry measurements. The algorithm accepts any algebraic effective viscosity model, as long as the model is differentiable, and it can be extended to more complicated non-Newtonian fluids (e.g. Oldroyd-B fluid) if a viscoelastic model is incorporated into the N-S problem.