Scalable physics-guided data-driven component model reduction for steady Navier-Stokes flow

TL;DR

This paper extends component reduced order modeling (CROM) to nonlinear steady Navier-Stokes equations, enabling fast, scalable, and accurate simulations of complex fluid flows at large industrial scales.

Contribution

It introduces a nonlinear extension of CROM using tensorial and empirical quadrature methods for Navier-Stokes equations, significantly improving scalability and efficiency.

Findings

Achieved ~23.7x faster solutions

Maintained ~2.3% relative error

Scaled to problems 256 times larger

Abstract

Computational physics simulation can be a powerful tool to accelerate industry deployment of new scientific technologies. However, it must address the challenge of computationally tractable, moderately accurate prediction at large industry scales, and training a model without data at such large scales. A recently proposed component reduced order modeling (CROM) tackles this challenge by combining reduced order modeling (ROM) with discontinuous Galerkin domain decomposition (DG-DD). While it can build a component ROM at small scales that can be assembled into a large scale system, its application is limited to linear physics equations. In this work, we extend CROM to nonlinear steady Navier-Stokes flow equation. Nonlinear advection term is evaluated via tensorial approach or empirical quadrature procedure. Application to flow past an array of objects at moderate Reynolds number demonstrates $\sim23.7$ times faster solutions with a relative error of $\sim 2.3\%$, even at scales $256$ times larger than the original problem.