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

The cost of writing, transferring, and storing large amounts of data from unsteady simulations limits the accessibility of the entire solution, often leaving the majority of the flow under-sampled or not analyzed. For example, modeling the transient behavior of rare, but important, dynamic events requires three-dimensional snapshots written at high sampling rates, over a long duration. As such, the simulation time needed and large quantity of data produced, makes this a challenging problem for practical computational fluid dynamic (CFD) workflows, where memory resources are often limited and the writing penalty for modern GPU computing is much costlier. In this work, multiple sparse flow reconstruction (SFR) methods are developed to approximate a full unsteady solution by writing far fewer sparse measurements from the CFD solver, thus diminishing writing costs, data storage, and enabling greater sampling rates. SFR is motivated by a large-eddy simulation (LES) example pursuing rare inlet distortion events, demonstrating that a down-sampling in full snapshots, supplemented by high-frequency sparse measurements, can substantially reduce writing time for a GPU solver and nearly eliminate the writing cost for a CPU solver. In its simplest form, the “snapshot” SFR method is a single equation and can be further compressed with Proper Orthogonal Decomposition (POD-SFR) or its smaller and faster double POD-SFR variant. A streaming SFR modification reconstructs snapshots more efficiently when local memory cannot store the entire solution. A sensitivity study evaluates the SFR scaling trade-off between sparse sampling rates and reconstruction accuracy, outlining best practices. To offset error of using random sparse measurements, the SFR approach exactly preserves dynamics in designated flow regions by additionally specifying sparse measurement locations, used here to capture the inlet 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.