Robust and Scalable Projection-based Reduced-order Models for Simulations of Reacting Flows

Abstract

This thesis investigates the development and application of projection-based reduced-order models (PROMs) to mitigate the exorbitant computational cost of high-fidelity numerical simulations of complex systems. Traditionally, PROMs operate by learning a low-dimensional representation of the system state from a small amount of high-fidelity simulation data, projecting the governing equations onto a low-dimensional subspace, and evolving the resulting system on the low-dimensional manifold inexpensively. For advection-dominated and highly non-linear flows, classical PROMs are found to be deficient in reliably generating robust and accurate predictions of flows featuring multi-scale and multi-physics phenomena. Further, PROMs of non-linear systems require hyper-reduction methods to achieve significant computational cost savings, and such approaches have yet to be rigorously investigated in stiff and chaotic flow problems. The methods developed in this thesis are motivated by and applied to complex reacting flows, with a particular emphasis on rocket combustion.

This work evolves from the recent model-form preserving least-squares with variable transformation (MP-LSVT) method, which derives the ROM using a least-squares procedure, and simulates the dynamics with respect to an alternative state representation. This approach exhibits greatly improved accuracy and stability over classical PROM methods for reacting flow simulations. These techniques are then applied to a number of challenging multi-scale and reacting flow systems.

First, an open-source framework for implementing novel ROM approaches for 1D reacting flows, named the Prototyping Environment for Reacting Flow Order Reduction Methods (PERFORM), is outlined. This package is used to conduct a critical examination of several novel neural network ROM approaches is conducted for a model premixed flame case. This approach exhibits utility in enabling accurate representations of flows characterized by sharp gradients and propagating waves. Further, non-intrusive neural network ROM approaches are shown to greatly outperform comparable classical intrusive PROM methods. However, analysis of the cost of training these neural network models reveals that they are hardly an efficient solution compared to equivalent linear approximations.

Scalable hyper-reduced PROMs are developed within a massively parallel compressible reacting flow solver, and demonstrated for a 2D transonic flow over an open cavity, a 3D single-element rocket combustor, and a 3D nine-element rocket combustor. The effects of the sample mesh and hyper-reduction approximation dimension on PROM performance is probed at length. Recent algorithms for selecting sample points are shown to generate accurate models, while some methods used in the classical PROM literature are shown to generate unstable solutions. Over three orders of magnitude computational costs savings, while retaining simulation accuracy are realized. Further, the nine-element rocket combustor experiment represents the largest and most physically-complex system investigated to date, involving extreme stiffness and nearly 250 million degrees of freedom. However, the ultimate goal of PROMs is truly generalizable, predictive models. To this end, analyses are conducting for a recent adaptive PROM approach, revealing that future-state and parametric predictions are achievable for very long time horizons.

Finally, best practices for the development and application of PROMs are documented. These guidelines will hopefully inform future PROM practitioners and help mitigate costly trial-and-error efforts. In summary, this work shows that novel projection-based reduced-order models offer an attractive means to leverage an ever-growing ecosystem of numerical and experimental data to generate accurate and low-cost solutions.