A Bayesian approach to physics-based reconstruction of incompressible flows

Abstract

To reconstruct smooth velocity fields from measured incompressible flows, we introduce a statistical regression method that takes into account the mass continuity equation. It is based on a multivariate Gaussian process and formulated within the Bayesian framework, which is a natural framework for fusing experimental data with prior physical knowledge. The robustness of the method and its implementation to large data sets are addressed and compared to a method that does not include the incompressibility constraint. A two-dimensional synthetic test case is used to investigate the accuracy of the method and a real three-dimensional experiment of a circular jet in water is used to investigate the method’s ability to fill up a gap containing a vortex ring.