arXiv subjects

Shunxiang Cao

Publications and source records attributed to Shunxiang Cao.

5 recordsLinked to original sources

arXiv2026

A Hybrid POD-Autoencoder Framework for Reduced Order Modeling of Turbulent Flow via Strategic Field Decomposition

This study proposes a hybrid reduced-order modeling (ROM) framework for the simulation of turbulent flow. The central idea is to decompose flow dynamics according to their temporal characteristics and predict the resulting components individually. The full field is first divided into a sub-field represented by a limited number of proper orthogonal decomposition (POD) modes (named as POD-retained field) and the corresponding residual sub-field (named as POD-truncated field). A frequency-informed POD strategy identifies the retained modes by considering both modal energy and dominant frequency. The evolution of retained POD coefficients, which feature similar temporal scales, is described using a vector autoregressive (VAR) model. In parallel, the POD-truncated field is compressed into a low-dimensional latent space using a Fourier-neural-operator-based Koopman $β$-variational autoencoder (FK-$β$-VAE), with the latent variables subsequently predicted by a switching-VAR model. Turbulent statistics of the full field are recovered by combining the contributions from the two components. The framework is assessed using turbulent channel flow at a friction Reynolds number of $110$. The predicted Reynolds-stress components, turbulent kinetic energy (TKE), and dominant wavenumber spectra show good agreement with the reference. Moreover, in comparison with an alternative framework of full-field modeling (i.e., without field decomposition), the proposed framework yields more accurate and robust long-term statistical predictions.

physics.flu-dyn↗

arXiv2026

An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interaction

We propose an arbitrary Lagrangian-Eulerian (ALE)-consistent machine learning framework for long-term fluid-structure interaction (FSI) prediction on deforming unstructured meshes. Specifically, the fluid dynamics are modeled by a surrogate that combines a graph neural operator (GNO) with a vision Transformer (ViT) for spatiotemporal prediction, while a lightweight long short-term memory (LSTM) network predicts structural kinematics at the interface. The two surrogates are coupled through a standard partitioned procedure. Most importantly, kinematic compatibility at the moving interface is enforced via an ALE-consistent boundary-correction step that updates the fluid-side interface velocity with the predicted structural velocity at each coupling update, thereby improving near-interface accuracy and long-term rollout stability. To mitigate autoregressive error accumulation, a two-stage training strategy is adopted, consisting of single-step supervised pretraining followed by long-term autoregressive fine-tuning. The proposed framework is validated on the benchmark problem of a flexible beam vibration in the wake of a cylinder. Results demonstrate accurate phase-consistent predictions over long rollouts and robust generalization under inlet-profile variations in both interpolation and extrapolation settings. Systematic ablation studies further assess the respective contributions of the ViT module, ALE-consistent boundary correction, and long-term training to predictive accuracy and rollout robustness.

physics.flu-dyn↗

arXiv2025

B-spline periodization of Fourier pseudo-spectral method for non-periodic problems

Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems. The Chebyshev method mitigates this issue but requires edge-clustered grids, which does not match the characteristics of many physical problems. To overcome these restrictions, we propose a B-spline-periodized Fourier (BSPF) method that extends to non-periodic problems while retaining spectral-like accuracy and efficiency. The method combines a B-spline approximation with a Fourier-based residual correction. The B-spline component enforces the smooth matching of boundary values and derivatives, while the periodic residual is efficiently treated by Fourier differentiation/integration. This construction preserves spectral convergence within the domain and algebraic convergence at the boundaries. Numerical tests on differentiation and integration confirm the accuracy of the BSPF method superior to Chebyshev and finite-difference schemes for interior-oscillatory data. Analytical mapping further extends BSPF to non-uniform meshes, which enables selective grid refinement in regions of sharp variation. Applications of the BSPF method to the one-dimensional Burgers' equation and two-dimensional shallow water equations demonstrate accurate resolution of sharp gradients and nonlinear wave propagation, proving it as a flexible and efficient framework for solving non-periodic PDEs with high-order accuracy.

math.NA↗

arXiv2024

Onset instability of inverted flags clamped by a cylinder

We numerically investigate the hydrodynamic characteristics and analyze the instability mechanism of a two-dimensional inverted flag clamped by a cylinder. Two transition routes and a total of six kinds of solutions exist under this configuration for different diameters of cylinders due to complex bifurcations. Specifically, for small cylinders, the undeformed equilibrium transitions to static deformed equilibrium through a supercritical pitchfork bifurcation, which is judged by the weakly nonlinear analysis together with the global linear instability analysis. The instability mechanism is the lifting effect of the steady structure mode working at the leading edge of the elastic plate. For large cylinders, another unstable fluid mode (decoupled with structure mode) causes the disappearance of the static undeformed and deformed equilibrium, replaced by a small amplitude flapping. The structure mode and the flow mode mainly contribute to the growth of perturbations in plate and downstream cylinder regions respectively, which can excite multi-mode oscillating transition analyzed by proper orthogonal decomposition. Moreover, we find there is a critical diameter $D_c$ dividing the pitchfork bifurcation and Hopf bifurcation, and $D_c$ decreases with the increase of Reynolds number. Finally, we prove downstream vortex shedding can induce upward vortex-induced vibration of the plate and further improve the efficiency of energy transfer from the fluid to the structure during small-deflection flapping.

physics.flu-dyn↗

arXiv2021

Bayesian Calibration for Large-Scale Fluid Structure Interaction Problems Under Embedded/Immersed Boundary Framework

Bayesian calibration is widely used for inverse analysis and uncertainty analysis for complex systems in the presence of both computer models and observation data. In the present work, we focus on large-scale fluid-structure interaction systems characterized by large structural deformations. Numerical methods to solve these problems, including embedded/immersed boundary methods, are typically not differentiable and lack smoothness. We propose a framework that is built on unscented Kalman filter/inversion to efficiently calibrate and provide uncertainty estimations of such complicated models with noisy observation data. The approach is derivative-free and non-intrusive, and is of particular value for the forward model that is computationally expensive and provided as a black box which is impractical to differentiate. The framework is demonstrated and validated by successfully calibrating the model parameters of a piston problem and identifying the damage field of an airfoil under transonic buffeting.

math.NA↗