Scalable and Predictive Model Order Reduction for Reacting Flow Systems

Abstract

Accurate, efficient prediction of reacting flow systems is challenging due to stiff reaction kinetics, significant disparity in spatiotemporal scales, and multi-physics interactions. Predictive tools for modeling these problems involve large-scale simulations in the form of prohibitively expensive direct numerical simulations (DNS) or slightly less expensive large-eddy simulations (LES), which can take weeks or months to run. Industry design cycle analysis requires rapid turnaround in minutes or hours, making them unsuitable for practical use. A grand challenge is, therefore, to inherit the predictive capabilities of a highly complex large-scale computation at a significantly reduced cost.

Projection-based reduced-order models - which aim for mathematically formal complexity reduction without sacrificing physical fidelity - have increased in popularity over the past two decades. These techniques have mostly been demonstrated to be successful on relatively simple problems. This thesis aims to make strides in utilizing projection-based reduced-order modeling on reacting flow systems, focusing on accuracy and scalability.

In the application of ROMs for larger-scale problems, it becomes clear that basic linear algebra pre-processing operations of large dense matrices present a significant hurdle. To better enable the development of large-scale ROMs, a software tool PLATFORM (Parallel Linear Algebra Tool FOr Reduced Modeling), has been developed to address these challenges. In addition to enabling the required distributed linear algebra, PLATFORM uses efficient I/O strategies to reduce the processing time of large data sets. This tool is ubiquitous throughout this work and critical for ROM development shown in this and other collaborative works.

An LES study of a Gas-Turbine Model Combustor (GTMC) is conducted using a flamelet-based turbulent combustion model for two operating conditions. These cases are quantitatively compared with experimental data and show good agreement. These simulations are used as a testbed for reduced-order model development. The highly chaotic nature of the GTMC system makes static basis methods unsuitable for any truly predictive or parametric ROM. Adaptive basis techniques are applied to mitigate this shortcoming by updating the projection sub-space as the dynamics evolve. This update is guided by the residual of the full order model operator, applied to the GTMC, and shown to successfully predict future state dynamics with very few training data snapshots. The significant reduction in offline training requirements and improved accuracy are critical components to enable the application of these ROMs in a design environment.

Next, an adaptive sampling method is used to achieve computational efficiency in conjunction with the predictive capability. This method is shown to maintain accuracy in predictive tasks while significantly reducing computational costs. However, online adaptation imposes a significant challenge in parallel load balancing, which limits scalability. A framework is proposed where the sampled ROM mesh points are dynamically distributed among MPI processes during runtime. This redistribution introduces a trade-off between the cost of load balancing and the savings achieved during the sampling iteration. The framework is demonstrated on reacting flow benchmarks and quantifies the improved computational speed-up and predictive capability.

These advances in ROM methods show that the grand challenge of truly predictive and scalable ROMs for complex problems is within reach. This work makes strides in applying these methods to large-scale problems and addressing practical challenges in a high-performance computing environment. Based on the achieved efficiency and predictive capability, the author believes this work will inform and assist in developing future production-level full and reduced-order solvers.