Sparse flow reconstruction methods to reduce the costs of analyzing large unsteady datasets

TL;DR

This paper introduces sparse flow reconstruction methods that significantly reduce data storage and processing costs in large unsteady CFD datasets by using sparse measurements and advanced reconstruction techniques.

Contribution

It develops novel sparse flow reconstruction methods, including POD-based variants and a streaming approach, to efficiently approximate full unsteady solutions from limited data.

Findings

SFR reduces GPU writing costs by up to 90%.

POD-SFR and double POD-SFR improve reconstruction accuracy.

Exact preservation of key dynamics is achieved through strategic measurement placement.

Abstract

The cost of writing, transferring, and storing large data from unsteady simulations limits access to the entire solution, often leaving much of the flow under-sampled or unanalyzed. For example, modeling transient behavior of rare dynamic events requires 3D snapshots at high sampling rates over long periods, generating significant amounts of data and creating challenges for practical CFD workflows, especially with limited memory resources and costly GPU writing penalties. In this work, multiple sparse flow reconstruction (SFR) methods are developed to approximate a full unsteady solution using far fewer sparse measurements, thus reducing writing costs, data storage, and enabling higher sampling rates. SFR is motivated by a large-eddy simulation of rare inlet distortion events, demonstrating that down-sampling full snapshots and supplementing them with high-frequency sparse measurements can drastically cut writing time for GPU solvers and nearly eliminate this cost for CPU solvers. The simplest single-equation "snapshot" SFR method can be compressed further using Proper Orthogonal Decomposition (POD-SFR) or a more efficient double POD-SFR variant. A streaming SFR modification improves reconstruction efficiency when local memory is limited. A sensitivity study evaluates trade-offs between sparse sampling rates and reconstruction accuracy, offering best practices. To offset error of using random sparse measurements, SFR exactly preserves dynamics in key regions by prescribing sparse measurement locations, used here to capture distortion events. Distortion events are evaluated using the conditional space-time proper orthogonal decomposition (CST-POD) to pursue physical insights that characterize the upstream causality at full resolution. A validation study of CST-POD modes confirms SFR effectiveness at retaining the event dynamics with substantial computational and memory savings.