Projection-based and neural-net reduced order model for nonlinear Navier–Stokes equations

Abstract

This paper presents complete steps for the construction and solution algorithm for a projection-based reduced order model coupled with an artificial neural net model. The reduced model is constructed based on the Galerkin projection of the equations governing the physical processes on reduced subspaces obtained by the Proper Orthogonal Decomposition method. The projection is done using numerical discretisation schemes implemented in the commonly used OpenFOAMⓇ platform. The neural net model is trained using the Nonlinear AutoRegressive eXogenous model network (NARX) architecture. The reduced order models are demonstrated for true predictions of incompressible flows at low Reynolds numbers driven by various boundary conditions. Compared with the full CFD simulations, this model shows excellent agreement while only requiring a fraction of the computational resources.