Wavelet Adaptive Proper Orthogonal Decomposition for Large Scale Flow Data

TL;DR

This paper introduces a wavelet-adaptive proper orthogonal decomposition (wPOD) method that efficiently processes high-resolution flow data by combining wavelet compression with POD, enabling scalable analysis of complex fluid flows.

Contribution

The paper presents a novel wavelet-based adaptive POD approach that reduces computational complexity and improves scalability for large-scale flow data analysis.

Findings

Efficient processing of high-resolution flow data demonstrated.

Balanced error control between wavelet compression and POD truncation.

Successful application to 2D wake flow and 3D insect flight data.

Abstract

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by three-dimensional direct numerical simulations, is limited owing to its computational complexity. Here, we propose a wavelet-based adaptive version of the POD (the wPOD), in order to overcome this limitation. The amount of data to be analyzed is reduced by compressing them using biorthogonal wavelets, yielding a sparse representation while conveniently providing control of the compression error. Numerical analysis shows how the distinct error contributions of wavelet compression and POD truncation can be balanced under certain assumptions, allowing us to efficiently process high-resolution data from three-dimensional simulations of flow problems. Using a synthetic academic test case, we compare our algorithm with the randomized singular value decomposition. Furthermore, we demonstrate the ability of our method analyzing data of a 2D wake flow and a 3D flow generated by a flapping insect computed with direct numerical simulation.