Scalable Projection-Based Reduced-Order Models for Large Multiscale Fluid Systems

Abstract

Although projection-based reduced-order models (PROMs) have existed for decades, they have rarely been applied to large, nonlinear, multiscale, and multi-physics systems due to the complexity of effectively implementing such methods. Advances in hyper-reduction have enabled the scalable computation of PROMs for general nonlinear dynamical systems. Further, the recent model-form-preserving least squares with variable transformation method has proven capable of generating stable PROMs for extremely stiff multiphysics problems. In this work, we formulate a PROM framework combining these methodologies and demonstrate that robust, accurate, and cost-effective PROMs can be realized for complex nonreacting and reacting compressible flows. Along with an open-source toolchain for hyper-reduction sample mesh generation from extremely large data sets, this represents an end-to-end effort to assess the applicability of PROMs to large-scale, multiphysics problems of engineering interest. We examine practical considerations for implementing hyper-reduction methods and their effect on memory consumption, load balancing, and interprocessor communications. These considerations produce accurate PROMs that are three to four orders of magnitude more computationally efficient than the full-order model in recreating transonic flow over a cavity and reacting flow in a rocket combustor. Guidelines for data preparation, sample mesh construction, and online PROM solution which promote robust simulations are also provided.