Non intrusive parametric Reduced Order Models based on physics for incompressible flow

Abstract

Reduced order modeling provides an efficient alternative to high fidelity simulations for the rapid prediction of fluid flows in many query settings. Among non intrusive approaches, Operator Inference (OpInf) enables the identification of reduced dynamical operators directly from data while preserving a prescribed mathematical structure. The present work extends physics structured OpInf to the construction of parametric Reduced Order Models for transient incompressible flows governed by the Navier-Stokes equations. The velocity and pressure fields are represented using separate global reduced bases, and their reduced operators are identified directly from temporal and parametric POD coefficients. The identification procedure is formulated as a sequence of uncoupled least squares problems, leading to an efficient offline stage while avoiding the explicit projection of the governing equations. The approach is first evaluated on a lid driven cavity flow in a periodic regime to assess temporal extrapolation and prediction at previously unseen parameter values. Its applicability is then demonstrated for transient flow through a porous medium with a square obstacle, for which the nonlinear terms are not directly amenable to a standard Galerkin projection. The results demonstrate that the approach can accurately reproduce both velocity and pressure fields while providing computationally efficient predictions for unseen parameter values.