Robust and globally efficient reduction of parametric, highly nonlinear computational models and real time online performance

Abstract

This paper considers the problem of parametric, nonlinear, projection-based model order reduction (PMOR) and makes three contributions to advance its state of the art. First, it presents a computational strategy for reducing the total offline cost of nonlinear PMOR by enabling hyperreduction to be performed adaptively within the typical greedy sampling procedure, rather than uniformly at each of its iteration. Then, it presents a more accurate and computationally efficient approach for training hyperreduction based on residual Jacobians rather than residuals. Finally, it demonstrates for a large-scale, industrial-grade, parametric, nonlinear application, that the two aforementioned contributions make both offline and online stages of nonlinear PMOR practical in today’s engineering environments. The paper also shows that despite the so-called Kolmogorov n-width barrier for the model reduction of convection-dominated transport problems, the current state of the art of nonlinear, Petrov–Galerkin PMOR equipped with the advances proposed in this paper is capable of accelerating by orders of magnitude the accurate solution of shape-parametric, high Reynolds number, viscous flow problems represented by the Reynolds-averaged Navier–Stokes equations augmented with turbulence modeling. All three contributions are presented and discussed in the contexts of steady-state CFD problems; however, they are equally applicable to unsteady CFD problems as well as problems in solid mechanics and structural dynamics.