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Surrogate models for multiregime flow problems

Jiyoung Lee1,*, Leon Chan1, Tony Zahtila2, Wilson Lu1, Gianluca Iaccarino2, and Andrew Ooi1

  • *Contact author: lee16@student.unimelb.edu.au
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Phys. Rev. Fluids 10, 024703 – Published 26 February, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.024703

Abstract

Surrogate modeling methods based on polynomial chaos expansion (PCE) and bifidelity (BF) approaches are investigated in the context of two-dimensional flow past two square cylinders. The overall wake behavior of this flow has been shown by Ma et al. [Phys. Fluids 29, 033604 (2017)] to give rise to multiple flow regimes with various vortex shedding patterns depending on the cylinder gap spacing, g*, and oncoming flow Reynolds number, Re. Within the scope of surrogate modeling, the possibility of multiple flow regimes occurring with varying input parameters forms an intriguing challenge, hence, the attempt in the present work to construct a model that will accurately reproduce the statistical quantities of the underlying physical flow regimes provides a distinction with typical reduced order models. We evaluate these surrogate models through statistical measures of their output with the ground-truth data collected from 200 Monte Carlo samples. Using the PCE-based methods, we are able to obtain highly accurate statistics and well-defined probability density functions (PDFs) but at a high overall cost in accordance with the findings reported in the preceding literature. Bifidelity approaches, by contrast, generate approximations to a large high-fidelity data-set by correcting low-fidelity (LF) solutions through a limited number of high-fidelity (HF) solutions. In this paper, LF models are constructed by using a dramatically reduced number of simulation grid points where the cost ratio of LF to HF simulation is O(10−3). We begin by using a multiplicative correction method where the mapping between low and high fidelity is achieved through a correction at randomized sample points. However, unreliable and inaccurate solutions are obtained, which provides a motivation to employ rank-revealing interpolative decomposition (ID) within the BF framework. More than just accurately approximating the high-fidelity data, our results show that ID can correctly classify physics in the solution space and identify the transition boundaries between flow regimes. By investigating multiple low-fidelity models, we find that increasing mesh resolution lowers the rank in our interpolative decomposition procedure and also the reconstruction error of the original LF matrix. We suggest that ID would allow purposeful and efficient uncertainty quantification methods, sensitivity analysis, and optimization for problems involving multiple modes of outcome or high-dimensional uncertainties.

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Phys. Rev. Fluids 10, 024703– Published 26 February, 2025
  • Received 23 June 2024
  • Accepted 4 February 2025
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