arXiv subjects

Zhaolong Han

Publications and source records attributed to Zhaolong Han.

13 recordsLinked to original sources

arXiv2026

On optimal convergence rates for parametrized variational problems with applications to nonlocal models

We develop an abstract variational framework for convergence rates of parametrized problems and their Galerkin approximations, with applications to nonlocal diffusion. The main objective is to quantify modeling and discretization errors in terms of the nonlocal horizon, the mesh size, the Sobolev regularity of the local solution, and the compatibility of boundary data. We establish error estimates in energy and $L^2$ norms and develop an adaptation of the Aubin--Nitsche argument that uses regularity of the limiting local dual problem. This approach yields improved $L^2$ estimates without requiring additional regularity of the nonlocal dual solutions, including for integrable kernels. We apply the framework to two constant-horizon nonlocal Laplacians with exterior boundary data and to heterogeneous localization models with classical Dirichlet, Neumann, and Robin conditions. The resulting estimates provide quantitative guarantees of asymptotic compatibility and improve existing error bounds under weaker regularity assumptions. Numerical experiments illustrate the convergence rates and examine the sharpness of the estimates.

math.NA↗

arXiv2026

A Graph-informed Kriging model for sample-efficient Bayesian optimization of wind farm layouts

Wind farm layout optimization becomes increasingly difficult as turbine count grows, especially when high-fidelity aerodynamic models are used. Conventional Kriging-based Bayesian optimization often suffers from low sample efficiency in high-dimensional layout spaces because sparse training data provide limited domain coverage. We develop a Graph-informed Kriging framework that embeds reusable aerodynamic interaction information into the surrogate mean function. The wind farm is represented as a directed aerodynamic graph, where pairwise turbine interactions defined in a low-dimensional relative-coordinate space are assembled into a farm-scale mean. This structured mean captures the dominant variation in annual energy production (AEP), allowing the Gaussian process to model only the residual structure and uncertainty. Numerical experiments show that Graph-informed Kriging consistently improves AEP prediction accuracy over ordinary and generic-trend Kriging under sparse-data conditions, with increasing benefits as layout dimension and wake-interaction strength grow. Embedded in Bayesian optimization, it substantially improves sample efficiency and achieves competitive solutions for the IEA Wind Task 37 benchmark with about 280 AEP evaluations. In a controlled 16-turbine case, it also outperforms ordinary and multi-fidelity Kriging under the same high-fidelity evaluation budget. The framework is further extended to a 48-turbine wind farm, demonstrating applicability to large-scale CFD-based layout optimization. These results show that Graph-informed surrogate modeling can enable more efficient use of high-fidelity aerodynamic models for reliable large-scale wind farm layout design.

cs.LG↗

arXiv2026

Six-Degree-of-Freedom Rotor-Load Cross-Spectral Density from Rotor-Plane Turbulence Cross-Spectra

A frequency-domain response analysis of a wind turbine rotor requires the complete hub-load spectrum, but the customary scalar thrust and torque spectra retain neither the four in-plane components nor the coupling between them. This paper derives the full six-degree-of-freedom (6-DOF) rotor-load cross-spectral-density (CSD) matrix from the IEC Kaimal turbulence model. By decoupling the spatial order of inflow coherence from the temporal Doppler shift, the formulation introduces a two-index rotational-sampling kernel. Rotor symmetry and azimuthal averaging constrain the observed Doppler carrier strictly to blade-passing harmonics $pBf_{\mathrm{rot}}$, while the azimuthal aerodynamic transfer shifts the spatial coherence order to $pB+s$. A convergence study of the retained azimuthal order $s$ shows that $\lvert s\rvert\le4$ suffices, the assembled CSD then deviating from the full-band result by less than $10^{-5}$ in relative norm. The formulation is compared with OpenFAST simulations of a rigid floating wind turbine over nine wind speeds: the six auto-spectral densities agree closely below 1~Hz, and the present theory over-predicts the spectra near the 6P and 9P rotational harmonics.

physics.flu-dyn↗

arXiv2025

On parameterized nonlocal-fractional transmission problems and associated function spaces

In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a fractional type Dirichlet energy on one subdomain and a nonlocal Dirichlet energy involving a finite range of interactions on another subdomain. We present the rigorous mathematical formulation and its well-posedness. We also investigate the behavior of the model in various limiting regimes.

math.AP↗

arXiv2024

Compactness results for a Dirichlet energy of nonlocal gradient with applications

We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic compact embedding of the associated nonlocal function spaces into the class of square-integrable functions. Moreover, we will demonstrate that the sequence of nonlocal function spaces converges in an appropriate sense to a limiting function space. As an application, we prove uniform Poincaré-type inequalities for sequence of half-space gradient operators. We also apply the compactness result to demonstrate the convergence of appropriately parameterized nonlocal heterogeneous anisotropic diffusion problems. We will construct asymptotically compatible schemes for these type of problems. Another application concerns the convergence and robust discretization of a nonlocal optimal control problem.

math.AP↗

arXiv2024

High-flexibility reconstruction of small-scale motions in wall turbulence using a generalized zero-shot learning

This study proposes a novel super-resolution (or SR) framework for generating high-resolution turbulent boundary layer (TBL) flow from low-resolution inputs. The framework combines a super-resolution generative adversarial neural network (SRGAN) with down-sampling modules (DMs), integrating the residual of the continuity equation into the loss function. DMs selectively filter out components with excessive energy dissipation in low-resolution fields prior to the super-resolution process. The framework iteratively applies the SRGAN and DM procedure to fully capture the energy cascade of multi-scale flow structures, collectively termed the SRGAN-based energy cascade framework (EC-SRGAN). Despite being trained solely on turbulent channel flow data (via "zero-shot transfer"), EC-SRGAN exhibits remarkable generalization in predicting TBL small-scale velocity fields, accurately reproducing wavenumber spectra compared to DNS results. Furthermore, a super-resolution core is trained at a specific super-resolution ratio. By leveraging this pre-trained super-resolution core, EC-SRGAN efficiently reconstructs TBL fields at multiple super-resolution ratios from various levels of low-resolution inputs, showcasing strong flexibility. By learning turbulent scale invariance, EC-SRGAN demonstrates robustness across different TBL datasets. These results underscore EC-SRGAN potential for generating and predicting wall turbulence with high flexibility, offering promising applications in addressing diverse TBL-related challenges.

physics.flu-dyn↗

arXiv2024

Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications

This work contributes to nonlocal vector calculus as an indispensable mathematical tool for the study of nonlocal models that arises in a variety of applications. We define the nonlocal half-ball gradient, divergence and curl operators with general kernel functions (integrable or fractional type with finite or infinite supports) and study the associated nonlocal vector identities. We study the nonlocal function space on bounded domains associated with zero Dirichlet boundary conditions and the half-ball gradient operator and show it is a separable Hilbert space with smooth functions dense in it. A major result is the nonlocal Poincaré inequality, based on which a few applications are discussed, and these include applications to nonlocal convection-diffusion, nonlocal correspondence model of linear elasticity, and nonlocal Helmholtz decomposition on bounded domains.

math.AP↗

arXiv2023

An optimization framework for wind farm layout design using CFD-based Kriging model

Wind farm layout optimization (WFLO) seeks to alleviate the wake loss and maximize wind farm power output efficiency, and is a crucial process in the design of wind energy projects.Since the optimization algorithms typically require thousands of numerical evaluations of the wake effects, conventional WFLO studies are usually carried out with the low-fidelity analytical wake models.In this paper, we develop an optimization framework for wind farm layout design using CFD-based Kriging model to maximize the annual energy production (AEP) of wind farms. This surrogate-based optimization (SBO) framework uses latin hypercube sampling to generate a group of wind farm layout samples, based on which CFD simulations are carried out to obtain the corresponding AEPs.This wind farm layout dataset is used to train the Kriging model, which is then integrated with an optimizer based on genetic algorithm (GA). As the optimization progresses, the intermediate optimal layout designs are again fed into the dataset.Such adaptive update of wind farm layout dataset continues until the algorithm converges.To evaluate the performance of the proposed SBO framework, we apply it to three representative wind farm cases.Compared to the conventional staggered layout, the optimized wind farm produces significantly higher total AEP.In particular, the SBO framework requires significantly smaller number of CFD calls to yield the optimal layouts that generates almost the same AEP with the direct CFD-GA method.Further analysis on the velocity fields show that the optimization framework attempts to locate the downstream turbines away from the the wakes of upstream ones.The proposed CFD-based surrogate model provides a more accurate and flexible alternative to the conventional analytical-wake-model-based methods in WFLO tasks, and has the potential to be used for designing efficient wind farm projects.

physics.flu-dyn↗

arXiv2023

Aerodynamic performance enhancement and noise reduction for Darrieus vertical axis wind turbines: V-shaped blades and trailing-edge serrations

The Darrieus vertical axis wind turbines (VAWTs) are one of the mainstream devices for wind energy utilization in the urban areas. The market's pursuit of high wind energy conversion efficiency promotes the research on improving the wind turbine power coefficient while reducing noise. This paper makes further investigation on the aerodynamics and aeroacoustics of a small VAWT with V-shaped blades and trailing-edge serrations. The feasibility of utilizing the Reynolds-Averaged Navier-Stokes SST k-omega turbulence model and the FW-H method is verified against experiments. The studied V-shaped blades can effectively improve the power performance of VAWT over a wide range of tip speed ratios under normal wind speed conditions, and the trailing-edge serrations will also slightly increase the power output of V-bladed VAWT at the optimal tip speed ratio. The power coefficient of the V-bladed wind turbine with trailing-edge serrations is about 28.3% higher than that of the original turbine. In addition, a dumbbell-shaped noise directivity distribution was first discovered in the VAWT compared with the traditional elliptical distribution. The V-bladed VAWT generated less low-frequency noise and the trailing-edge serrations realized the expected noise reduction effect. Practically, this study proposes a feasible solution for the design of high-efficiency and low-noise wind turbines.

physics.flu-dyn↗

arXiv2023

Aerodynamic characterization of two tandem wind turbines under yaw misalignment control using actuator line model

Yaw control has proven to be promising in alleviating the wake effects that plague the efficiency of wind farms. In this work, the actuator line modeling (ALM) method is adopted to simulate the flows over two tandem turbines distanced by $3 - 7$ rotor diameters, with the yaw angle of the upstream rotor varying from $γ_1=0^{\circ}$ to $50^{\circ}$. The aim is to provide a comprehensive aerodynamic characterization of a simple wind farm under yaw misalignment. With increasing yaw angle, the power generated by the downstream rotor increases, compensating the power loss in the upstream rotor, and resulting in higher total power of the two turbines than that without yaw control. The maximum power output is achieved as the upstream wake of the yawed rotor is redirected away from the downstream rotor plane. Behind the downstream rotor, the secondary steering phenomenon is observed, where the wake is also redirected from the centerline. The use of the actuator line model also reveal unsteady aerodynamic characteristics that can not be captured by lower-fidelity models. For the upstream rotor, the yaw misalignment results in time-varying change in the local angle of attack on the blade, giving rise to unsteady loading. The downstream rotor is partially submerged in the deflected wake incurred by the yawed upstream rotor. As the blade revolves into and out of the wake deficit, the blade experiences cyclic loading, leading to even stronger fluctuations in the aerodynamic loads than the upstream rotor. These analysis provides a comprehensive understanding of the yaw control effects on the two tandem rotors from the perspectives of aerodynamic performance, wake profiles, and unsteady characteristics. The insights gained from the study can aid the design of collective yaw control strategies of wind farms, and lay the foundation for assessing the fatigue damage associated with yaw misalignment.

physics.flu-dyn↗

arXiv2022

End boundary effects on wakes dynamics of inclined circular cylinders

We perform direct numerical simulations to characterize the three-dimensional wake dynamics of long inclined circular cylinders with inhomogeneous end boundary conditions. Three Reynolds numbers, $\Rey=100$, 200 and 300 are considered to reveal the roles of the intrinsic secondary instabilities and the extrinsic end boundary effects in shaping the three-dimensional flows. At $\Rey=100$, the end boundary effects are felt over the entire cylinder span by inducing oblique vortex shedding, which is associated with stronger spanwise flow in the wake than a parallel shedding. The Strouhal number of the oblique shedding is related to that of the parallel shedding of straight cylinder by the cosine law, considering the combined inclination angle and oblique angle. At $\Rey=200$, the intrinsic secondary instability results in large-scale vortex dislocation, precluding the propagation of the end boundary effects towards further span. Nevertheless, for the inclined cases, oblique shedding is still observed within limited span from the upstream end boundary. The oblique vortices are related to the two-dimensional flow at $\Rey=200$ from the viewpoint of cosine law. Further along the span, the oblique vortices destabilizes with the formation of small-scale vortices, and the flow transitions to the typical mode A* wake. At $\Rey=300$, the highly three-dimensional flow near the end boundary creates disturbances that travel along the cylinder span, creating vortex dislocations for cases with low inclination angles. For high inclination angle, oblique vortex shedding is again observed over the cylinder span, and is not disrupted by vortex dislocations of either intrinsic or extrinsic causes.

physics.flu-dyn↗

arXiv2022

Turbulence suppression by streamwise-varying wall rotation in pipe flow

Direct numerical simulations (DNSs) of turbulent pipe flow subjected to streamwise-varying wall rotation are performed. This control method is able to achieve drag reduction and even relaminarize the flow under certain control parameters at low Reynolds number. Two control parameters, which are velocity amplitude and wavelength, are considered. An annular boundary layer, called Spatial Stokes Layer (SSL), is formed by the wall rotation. Based on the thickness of SSL, two types of drag reduction scenarios are identified. When the thickness is low, the SSL acts as a spacer layer, obstructing the impact of fluids against the wall and hence reducing the shear stress. The flow structures in the outer layer are less affected and are stretched in streamwise direction due to the increased velocity gradient. Within the SSL, the turbulence intensity diminishes dramatically. When the thickness is large, a streamwise wavy pattern of near-wall low-speed streaks is formed. The orientation of streaks is found to lag behind the direction of local mean velocity in phase and conform to the direction of local resultant shear stress. The streamwise scale of near-wall flow structures is significantly reduced, resulting in the disruption of downstream development of flow structures and hence leading to the drag reduction. Besides, it is found that it requires both large enough thickness of SSL and velocity amplitude to relaminarize the turbulence. The relaminarization mechanism is that the annular SSL can continuously absorb energy from wall-normal stress due to the rotation effect, thereby the turbulence self-sustaining process could not be maintained. For the relaminarization cases, the laminar state is stable to even extremely large perturbations, which possibly makes laminar state the only fixed point for the whole system.

physics.flu-dyn↗

arXiv2019

Bistability in the wake of a wavy cylinder

We investigate the wake dynamics of an optimally designed wavy cylinder that completely suppresses the Kármán vortex shedding. Such a wavy cylinder is forced to oscillate with a sinusoidal motion in the crossflow direction. Examination of the lift force spectrum reveals that a critical forcing frequency exists, below which the flow control effectiveness of the wavy cylinder is retained, and beyond which the inherent vortex shedding resurrects. Moreover, the resurrected unsteady vortex shedding can persist even without sustained forcing, leading to the loss of control efficacy. This suggests that in addition to the steady state developed from uniform initial condition, an oscillatory state exists in the wake of wavy cylinder if the initial state is sufficiently perturbed. The discovery of the bistable states calls for examination of the flow control effectiveness of the wavy cylinder in more complicated inflow conditions.

physics.flu-dyn↗