arXiv subjects

Jiaqing Kou

Publications and source records attributed to Jiaqing Kou.

16 recordsLinked to original sources

arXiv2026

Optimization-Based Discovery of A Non-Attracting Flow State in An Oscillating-Cylinder Wake

In the flow past a stationary circular cylinder, the classical Karman vortex street arises from a Hopf bifurcation of the steady flow at the critical Reynolds number. Although this solution becomes dynamically unstable beyond this point, it remains an exact solution of the governing equations. Motivated by this observation, we investigates whether similar non-attracting flow solutions exist in the flow past a forced oscillating cylinder at supercritical Re. In the present study, while employing PINNs to investigate the flow past a forced oscillating cylinder, we identify a class of flow solutions that are inaccessible through direct time-stepping simulations. The obtained solution remains phase-locked with the cylinder oscillation frequency, despite the corresponding parameters lying outside the lock-in regime. To verify this solution, the obtained PINNs solution is used as the initial guess for an optimization based on the optimizing a discrete loss (ODIL) framework. The results show that the solution can be consistently maintained during the optimization process. This indicates that the solution is self-consistent in the optimization sense, although it does not an attracting state of the original dynamical system. To understand the reason, we compare the numerical evolution mechanisms of each solvers. The results indicate that, flow states that satisfy the governing equations but are dynamically non-attracting can be identified and maintained as minima of the optimization problem. For the flow past a forced oscillating cylinder, non-attracting periodic solutions that satisfy the governing equations exist in addition to the attracting states obtained by conventional time-stepping simulations. Optimization-based solvers can therefore reveal such flow states that are difficult to obtain through direct time integration, providing a new perspective for understanding complex wake dynamics.

physics.flu-dyn↗

arXiv2025

A High-Order Immersed Boundary Method for Fluid-Structure Interaction Problems

Accurate and efficient simulation of fluid-structure interaction (FSI) problems remains a central challenge in computational physics. High-order discontinuous Galerkin (DG) methods offer low numerical errors and excellent scalability on modern architectures, making them attractive for high-fidelity FSI simulations. This study presents a high-order immersed boundary method (IBM) for FSI problems which combines a volume-penalization approach with a high-order nodal DG solver. To improve near wall accuracy, an anisotropic p-adaptation strategy based on reinforcement learning is used to dynamically adjust the polynomial orders in the mesh elements located near the moving immersed boundaries. By doing so, we show enhanced accuracy with a limited increase in computational cost. Accurate evaluation of surface forces is achieved using symmetric high-order Gaussian quadrature on immersed boundaries. The proposed method is coupled with both rigid-body and elastic-structure solvers within a partitioned framework. Numerical validations using a pitching airfoil, stall flutter of an airfoil, and flow-induced vibration of an elastic beam behind a cylinder demonstrate high-order accuracy and robustness. These results indicate that the present approach provides an effective and scalable strategy for complex moving-boundary FSI simulations.

physics.flu-dyn↗

arXiv2025

Goal-oriented Feature Extraction: a novel approach for enhancing data-driven surrogate model

Surrogate model can replace the parametric full-order model (FOM) by an approximation model, which can significantly improve the efficiency of optimization design and reduce the complexity of engineering systems. However, due to limitations in efficiency and accuracy, the applications of high-dimensional surrogate models are still challenging. In the present study, we propose a method for extracting hidden features to simplify high-dimensional problems, thereby improving the accuracy and robustness of surrogate models. We establish a goal-oriented feature extraction (GFE) neural network through indirect supervised learning. We constrained the distance between hidden features based on the differences in the target output. This means that in the hidden feature space, cases that are closer in distance output approximately the same, and vice versa. The proposed hidden feature learning method can significantly reduce the dimensionality and nonlinearity of the surrogate model, thereby improving modeling accuracy and generalization capability. To demonstrate the efficiency of our proposed ideas, We conducted numerical experiments on three popular surrogate models. The modeling results of typical high-dimensional mathematical cases and aerodynamic performance cases of ONERA M6 wings show that goal-oriented feature extraction significantly improves the modeling accuracy. Goal-oriented feature extraction can effectively reduce the error distribution of predicting cases and reduce the convergence and robustness differences caused by various data-driven surrogate models.

physics.flu-dyn↗

arXiv2024

PINN-MG: A Multigrid-Inspired Hybrid Framework Combining Iterative Method and Physics-Informed Neural Networks

Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have emerged as a novel approach for solving PDEs, with studies revealing that they exhibit faster convergence for low-frequency components. Building on this complementary frequency convergence characteristics of iterative methods and neural networks, we draw inspiration from multigrid methods and propose a hybrid solving framework that combining iterative methods and neural network-based solvers, termed PINN-MG (PMG). In this framework, the iterative method is responsible for eliminating local high-frequency oscillation errors, while Physics-Informed Neural Networks (PINNs) are employed to correct global low-frequency errors. Throughout the solving process, high- and low-frequency components alternately dominate the error, with each being addressed by the iterative method and PINNs respectively, thereby accelerating the convergence. We tested the proposed PMG framework on the linear Poisson equation and the nonlinear Helmholtz equation, and the results demonstrated significant acceleration of the PMG when built on Gauss-Seidel, pseudo-time, and GMRES methods. Furthermore, detailed analysis of the convergence process further validates the rationality of the framework. We proposed that the PMG framework is a hybrid solving approach that does not rely on training data, achieving an organic integration of neural network methods with iterative methods.

physics.comp-ph↗

arXiv2023

A combined volume penalization / selective frequency damping approach for immersed boundary methods: application to moving geometries

This work extends, to moving geometries, the immersed boundary method based on volume penalization and selective frequency damping approach [J. Kou, E. Ferrer, A combined volume penalization/selective frequency damping approach for immersed boundary methods applied to high-order schemes, Journal of Computational Physics (2023)]. To do so, the numerical solution inside the solid is decomposed into a predefined movement and an oscillatory part (spurious waves), where the latter is damped by an SFD approach combined with volume penalization. We challenge the method with two cases. First, a new manufactured solution problem is proposed to show that the method can recover high-order accuracy. Second, we validate the methodology by simulating the laminar flow past a moving cylinder, where improved accuracy of the combined method is reported.

physics.flu-dyn↗

arXiv2022

A modified equation analysis for immersed boundary methods based on volume penalization: applications to linear advection-diffusion and high-order discontinuous Galerkin schemes

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with high-order methods (e.g., discontinuous Galerkin). For this combination to be effective, an analysis of the numerical errors is essential. In this work, we apply, for the first time, a modified equation analysis to the combination of IBM (based on volume penalization) and high-order methods (based on nodal discontinuous Galerkin methods) to analyze a priori numerical errors and obtain practical guidelines on the selection of IBM parameters. The analysis is performed on a linear advection-diffusion equation with Dirichlet boundary conditions. Three ways to penalize the immerse boundary are considered, the first penalizes the solution inside the IBM region (classic approach), whilst the second and third penalize the first and second derivatives of the solution. We find optimal combinations of the penalization parameters, including the first and second penalizing derivatives, resulting in minimum errors. We validate the theoretical analysis with numerical experiments for one- and two-dimensional advection-diffusion equations.

math.NA↗

arXiv2022

Aeroacoustic airfoil shape optimization enhanced by autoencoders

We present a framework for airfoil shape optimization to reduce the trailing edge noise for the design of wind turbine blades. Far-field noise is evaluated using Amiet's theory coupled with the TNO-Blake model to calculate the wall pressure spectrum and fast turn-around XFOIL simulations to evaluate the boundary layer parameters. The computational framework is first validated using a NACA0012 airfoil at zero angle of attack. Particle swarm optimization is used to find the optimized airfoil configuration. The multi-objective optimization minimizes the A-weighted overall sound pressure level at various angles of attack, while ensuring enough lift and minimum drag. We compare classic parametrization methods to define the airfoil geometry (i.e., CST) to a machine learning method (i.e., a variational autoencoder). We observe that variational autoencoders can represent a wide variety of geometries, with only four encoded variables, leading to efficient optimizations, which result in improved optimal shapes. When compared to the baseline geometry, a NACA0012, the autoencoder-based optimized airfoil reduces by 3% (1.75 dBA) the overall sound pressure level (with decreased noise across the entire frequency range), while maintaining favorable aerodynamic properties in terms of lift and drag.

physics.flu-dyn↗

arXiv2022

Jump penalty stabilisation techniques for under-resolved turbulence in discontinuous Galerkin schemes

Jump penalty stabilisation techniques have been recently proposed for continuous and discontinuous high order Galerkin schemes [1,2,3]. The stabilisation relies on the gradient or solution discontinuity at element interfaces to incorporate localised numerical diffusion in the numerical scheme. This diffusion acts as an implicit subgrid model and stablises under-resolved turbulent simulations. This paper investigates the effect of jump penalty stabilisation methods (penalising gradient or solution) for stabilisation and improvement of high-order discontinuous Galerkin schemes in turbulent regime. We analyse these schemes using an eigensolution analysis, a 1D non-linear Burgers equation (mimicking a turbulent cascade) and 3D turbulent Navier-Stokes simulations (Taylor-Green Vortex problem). We show that the two jump penalty stabilisation techniques can stabilise under-resolved simulations thanks to the improved dispersion-dissipation characteristics (when compared to non-penalised schemes) and provide accurate results for turbulent flows. The numerical results indicate that the proposed jump penalty stabilise under-resolved simulations and improve the simulations, when compared to the original unpenalised scheme and to classic explicit subgrid models (Smagorisnky and Vreman).

physics.flu-dyn↗

arXiv2022

An experimental modal testing method for subcritical flow around a cylinder

Modal analysis of fluid flows is essential to understand flow physics and fluid-solid interaction mechanisms, and to implement flow control. Unlike unstable flow, the intrinsic attenuation of subcritical flow has led to failures to experimentally extract the subcritical flow modes clearly. To this end, this paper proposes a modal testing method for subcritical flows. Using Dynamic Mode Decomposition (DMD), dominate modes of flow around a cylinder at subcritical Reynolds numbers are extracted experimentally for the first time. The extracted structures and parameters of the modes are in good agreement with the numerical results in the literature. It is found that the first-order von Kármán mode can be observed at a Reynolds number as low as 19.3, which is very close to the lower boundary of subcritical vortex induced vibrations (VIV). This experimental observation elucidates the correlation between von Kármán mode and fluid-solid interaction instability in subcritical flows.

physics.flu-dyn↗

arXiv2021

Deep Learning for Multi-Fidelity Aerodynamic Distribution Modeling from Experimental and Simulation Data

The wind-tunnel experiment plays a critical role in the design and development phases of modern aircraft, which is limited by prohibitive cost. In contrast, numerical simulation, as an important alternative paradigm, mimics complex flow behaviors but is less accurate compared to experiment. This leads to the recent development and emerging interest in applying data fusion for aerodynamic prediction. In particular, the accurate prediction of aerodynamic with lower computational cost can be achieved by fusing experimental (high-fidelity) and computational (low-fidelity) aerodynamic data. Currently, existing works on aerodynamic model using data fusion mainly concern integral data (lift, drag, etc.). In this paper, a multi-fidelity aerodynamic model based on Deep Neural Network (DNN), where both numerical and experimental data are introduced in the loss function with proper weighting factor to balance the overall accuracy, is developed for aerodynamic distribution over the wing surface. Specially, the proposed approach is illustrated by modeling the surface pressure distribution of ONERA M6 wing in transonic flow, including different secnarios where the flow condition varies or there is less high-fidelity data. The results demonstrate that the proposed approach with decent number of low-fidelity data and a few high-fidelity data can accurately predict the surface pressure distribution on transonic wing. The outperformance of the proposed model over other DNNs from only high fidelity or low-fidelity, has been reported.

physics.flu-dyn↗

arXiv2021

Experimental study on Vortex-Induced Vibration of Cylinder at Subcritical Reynolds Number

Numerical simulation results in recent years show that vortex-induced vibration (VIV) can occur at a subcritical Reynolds number. And the VIV has been observed numerically at Reynolds numbers as low as Re = 20. The current study presents an experimental evidence for the subcritical VIV of a cylinder. We designed and built a rotating channel that makes it possible to perform VIV experiments at subcritical Reynolds numbers. Based on the rotating channel, two sets of tests were carried out for fixed natural frequency with variable incoming flow speed and fixed incoming flow speed with variable natural frequency. In both sets of experiments, subcritical VIV were observed and the VIV can be observed at a Reynolds number as low as 23, which is close to the numerical results of Mittal.

physics.flu-dyn↗

arXiv2021

A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemes

There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method to avoid body-fitted meshes and has been recently adapted to high order discretisations (Kou et al., 2021). This work proposes an improvement over the classic penalty formulation for flux reconstruction high order solvers. We include a selective frequency damping (SFD) approach (Aakervik et al., 2006) acting only inside solid body defined through the immersed boundary masking, to damp spurious oscillations. An encapsulated formulation for the SFD method is implemented, which can be used as a wrapper around an existing time-stepping code. The numerical properties have been studied through eigensolution analysis based on the advection equation. These studies not only show the advantages of using the SFD method as an alternative of the traditional volume penalization, but also show the favorable properties of combining both approaches. This new approach is then applied to the Navier-Stokes equation to simulate steady flow past an airfoil and unsteady flow past a circular cylinder. The advantages of the SFD method in providing improved accuracy are reported.

math.NA↗

arXiv2021

Eigensolution analysis of immersed boundary method based on volume penalization: applications to high-order schemes

This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR) discretization, including the influence of polynomial order and penalization parameter on numerical errors and stability. Through a semi-discrete analysis, we find that the inclusion of IBM adds additional dissipation without changing significantly the dispersion of the original numerical discretization. This agrees with the physical intuition that in this type of approach, the solid wall is modelled as a porous medium with vanishing viscosity. From a stability point view, the selection of penalty parameter can be analyzed based on a fully-discrete analysis, which leads to practical guidelines on the selection of penalization parameter. Numerical experiments indicate that the penalization term needs to be increased to damp oscillations inside the solid (i.e. porous region), which leads to undesirable time step restrictions. As an alternative, we propose to include a second-order term in the solid for the no-slip wall boundary condition. Results show that by adding a second-order term we improve the overall accuracy with relaxed time step restriction. This indicates that the optimal value of the penalization parameter and the second-order damping can be carefully chosen to obtain a more accurate scheme. Finally, the approximated relationship between these two parameters is obtained and used as a guideline to select the optimum penalty terms in a Navier-Stokes solver, to simulate flow past a cylinder.

math.NA↗

arXiv2019

Comparisons of Two Reduced-Order Models for Linearized Unsteady Aerodynamic Identification

This paper compares the performance of two unsteady aerodynamic reduced-order models (ROMs), namely linear Volterra series and the autoregressive with exogenous input (ARX) model, on modeling dynamically linear aerodynamic behaviors. The difference between these two methods is that the latter model has an autoregressive term while the former model has only the input-related term. The first system is a plunging cylinder in a low-Reynolds number flow, where the flow stable (Re < 47). Although the training data can be fitted well with both methods, the linear Volterra method requires a higher model order than the ARX model for the same accuracy. Comparison of the frequency response indicates that the ARX model approximates the frequency response more closely, while the frequency response at high Reynolds number is over-fitted by Volterra series. The second aerodynamic system is a flow over a pitching NACA0012 airfoil, including subsonic and transonic states. The convergence of the model with respect to delay orders, at different Mach numbers and mean angles of attack, is studied in detail. As the Mach number or the mean angle of attack increases, the required delay order will increase. But the ARX model still models this system with a small number of terms at the same level of accuracy. All results indicate that the ARX model outperforms the linear Volterra series in most of cases, especially when the flow is close to the unstable state.

physics.comp-ph↗

arXiv2018

Machine learning methods for turbulence modeling in subsonic flows over airfoils

Reynolds-Averaged Navier-Stokes(RANS) method will still play a vital role in the following several decade in aerospace engineering. Although RANS models are widely used, empiricism and large discrepancies between models reduce the reliability of simulating complex flows. Therefore, in recent years, data-driven turbulence model has aroused widespread concern in fluid mechanics. Based on the experimental/numerical simulation results, this approach aims to modify or construct the turbulence model for specific purposes by machine learning technologies. In this paper, we take the results calculated by SA model as training data. Different from low Reynolds number turbulent flows, the data from high Reynolds number flows shows an apparent scaling effect, thus leading to difficulties in the data-driven modeling. In order to improve the fitting accuracy, we divided the flow field into near-wall region, wake region, and far-field region, and built individual model for every region. In this paper, we adopted the radial basis function neural network (RBFNN) and some auxiliary optimization algorithms to reconstruct a mapping function between mean variables and the eddy viscosity. Since this model reflects the relationship between local flow characteristics and turbulent eddy viscosity, it is independent on the airfoil shape and flow condition. The training data in this paper is generated from only three subsonic flow calculations of NACA0012 airfoil. By coupling the proposed approach with N-S equations, we calculated various flow cases as well as two different airfoils and showed the eddy viscosity contours, velocity profiles along the normal direction of wall and skin friction coefficient distributions, etc. Compared with the SA model, the results show a reasonable accuracy and better efficiency, which indicates the positive prospect of data-driven methods in turbulence modeling.

physics.flu-dyn↗

arXiv2018

Mode Multigrid - A novel convergence acceleration method

This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of steady flow field according to the solution vectors from the previous time steps. Unlike the traditional multigrid method, we project the flowfield solutions from the physical space into the modal space, and truncate all the high-frequency modes but only the first-order mode are retained based on the DMD analysis. The real solutions in the physical space can be obtained simply by the inverse transformation from the modal space. The developed MMG method ingeniously avoids the complicated process of coarsening computational mesh, and does not need to make any change for the grid in physical space. Therefore, it is very convenient to be applied to any numerical schemes with just little change for the flow solver, which is also suitable for unstructured grids and easy for parallel computing. Several typical test cases have been used to verify the effectiveness of the proposed method, which demonstrates that the MMG can dramatically reduce the number of iterative steps for the different mesh types, different accuracy of spatial discretization and different time-marching schemes. The method is 3 to 6 times faster than the original method while ensuring the computational accuracy.

physics.comp-ph↗