Improvement of reduced-order model for two-dimensional cylinder flow based on global proper orthogonal decomposition in terms of robustness and computational speed

Abstract

Reduced-order models (ROMs) are widely used in fluid engineering to enable rapid prediction of flow fields for parametric analysis, design optimization, and control applications. Proper orthogonal decomposition (POD) is commonly employed to construct ROMs because it provides an optimal basis for representing a given flow dataset. However, POD-based ROMs often lack robustness when applied to flow conditions that differ from those included in the training data. Incorporating multiple flow conditions can improve robustness, but this generally increases the computational cost of ROM prediction, which limits practical applicability in engineering workflows. In this study, we propose a ROM framework that achieves fast and robust flow prediction even when the dataset contains a large number of flow conditions. The proposed approach employs a novel two-step order-reduction strategy based on POD. In the second reduction step, flow conditions that are most relevant to the target prediction are selectively retained, thereby reducing the computational cost without sacrificing accuracy. The performance of the proposed ROM is evaluated for a two-dimensional unsteady flow past a circular cylinder, a canonical benchmark problem in fluid engineering. The model accurately reproduces the relationship between vortex-shedding frequency and Reynolds number obtained from full numerical simulations. Furthermore, the proposed ROM reduces the computational cost by approximately 50% compared with a conventional POD-based ROM constructed using flow data at 27 different Reynolds numbers.

Figures (12)

• Figure 1: Computational grid and boundary conditions for flow around a circular cylinder.
• Figure 2: Reynolds number dependence of the Strouhal number for flow around a cylinder obtained by numerical simulation. The black line shows the Reynolds-Strouhal number curve in the HendersonHenderson, the red circle is the present result of full numerical simulation, the blue square is the DNS result of Jiang et al.cylinder4, and the green triangle is the experimental results of WilliamsonWilliamson_1989.
• Figure 3: Global POD modes obtained from a dataset containing a time series flow field with three Reynolds numbers. The first and second modes form a pair. The first and second modes form a pair. The presence of additional paired modes can be inferred from the spatial distributions of the third, seventh, and eighth modes. In contrast, the fifth mode does not form a pair with any other mode.
• Figure 4: Time variation of global POD mode coefficients at Reynolds number $55$ when ROM is constructed by changing the number of conditions in the dataset. The initial values for the coefficients are set to $0$. Full numerical results in the figure are computed from projecting the flow field into POD modes.
• Figure 5: Time variation of POD mode coefficients at Reynolds number $100$ when ROM is constructed by changing the number of conditions in the dataset in global POD.