Bayesian identification of a projection-based reduced order model for computational fluid dynamics

Abstract

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed.

Novel methodologies for solving the inverse unsteady heat transfer problem of estimating the boundary heat flux in continuous casting molds

“…In the future, it would also be interesting to investigate the use of a completely different approach in the solution of this inverse problem. Thinking about a more proper handling of the measurement noise, we could think of using a Bayesian approach 56 . Techniques such as ensemble Kalman filter could be suitable for this problem given the sequentiality of the measurements.…”

“…Thinking about a more proper handling of the measurement noise, we could think of using a Bayesian approach. 56 Techniques such as ensemble Kalman filter could be suitable for this problem given the sequentiality of the measurements. Moreover, considering the real‐time requirement of the application, it would probably require an effective use of model order reduction techniques to reduce the demanding computational cost of these techniques.…”