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

Seung Whan Chung, Youngsoo Choi, Pratanu Roy, Thomas Roy, Tiras Y. Lin, Du T. Nguyen, Christopher Hahn, Eric B. Duoss, Sarah E. Baker

TL;DR

CROM is extended to nonlinear steady Navier-Stokes flow equation via tensorial approach or empirical quadrature procedure, and application to flow past an array of objects at moderate Reynolds number demonstrates faster solutions.

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.

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

TL;DR

CROM is extended to nonlinear steady Navier-Stokes flow equation via tensorial approach or empirical quadrature procedure, and application to flow past an array of objects at moderate Reynolds number demonstrates faster solutions.

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 times faster solutions with a relative error of , even at scales times larger than the original problem.

Paper Structure

This paper contains 4 sections, 13 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Formulation
  3. Results
  4. Conclusion

Figures (1)

  • Figure 1: Scaled-up prediction of steady Navier-Stokes flow at $\nu=0.04$ over a $16\times16$ array of 5 different random objects: (left) flow-speed prediction of the proposed CROM; (top right) computation time with either (\ref{['eq:tensor']}) or (\ref{['eq:eqp']}), with respect to number of basis vectors; and (bottom right) relative error compared to the FOM solution, with respect to number of basis vectors. The error bar indicates $95\%$ confidence interval over 100 sample cases.