Efficient algorithm for proper orthogonal decomposition of block-structured adaptively refined numerical simulations

Abstract

Adaptive mesh refinement (AMR) is increasingly being used to simulate fluid flows that have vastly different resolution requirements throughout the computational domain. Proper orthogonal decomposition (POD) is a common tool to extract coherent structures from flow data and build reduced order models, but current POD algorithms do not take advantage of potential efficiency gains enabled by multi-resolution data from AMR simulations. Here, we explore a new method for performing POD on AMR data that eliminates repeated operations arising from nearest-neighbor interpolation of multi-resolution data onto uniform grids. We first outline our approach to reduce the number of computations with examples and provide the complete algorithms in the appendix. We examine the computational acceleration of the new algorithms compared to the standard POD method using synthetically generated AMR data and operation counting. We then use CPU times and operation counting to analyze data from an AMR simulation of an axisymmetric buoyant plume, finding that we are able to reduce the computational time by a factor of approximately 2 − 5 when using three levels of grid refinement. The new POD algorithm is the first to eliminate redundant operations for matrix multiplications with repeated values in each matrix, making it ideal for POD of data from AMR simulations.

Michael Meehan

Postdoctoral Research Associate

Mike is a former research associate in the Paul M. Rady Department of Mechanical Engineering at the University of Colorado Boulder and also a former student in the Turbulence and Energy Systems Laboratory, earned his PhD in May 2022.

Sam Simons-Wellin

PhD student

Sam’s research to date has been concerned with the design optimization and multiphysics computational model development of industrial scale materials processing systems in collaboration with 3M with the goal of studying material throughput, quality, system efficiency, process, and direct emissions. He further studies the mitigation of environmentally and societelly harmful combustion systems through the development of field-scale-deployable, accurate physical models that interface with advanced flow measurement diagnostics. Models developed to date have examined multifidelity approaches to capturing and describing molecular diffusion and mixing phenomena in fire scenarios as well as methane emission, destruction, and dispersion in polluting flaring systems. Sam incorporates modal decompositions and reduced order flow models that capture spatial and temporal dynamics from chemically and physically detailed simulations, and can be used in a computationally efficient framework to model large scale systems at industrial and weather scales.

Peter Hamlington

Associate Professor

Peter is an associate professor in the Paul M. Rady Department of Mechanical Engineering at the University of Colorado Boulder and the principal investigator of the Turbulence and Energy Systems Laboratory.