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Zhenhua Chai

Publications and source records attributed to Zhenhua Chai.

At least 37 records · Page 2Linked to original sources
arXiv2023

A consistent and conservative diffuse-domain lattice Boltzmann method for multiphase flows in complex geometries

Modeling and simulation of multiphase flows in complex geomerties are challenging due to the complexity in describing the interface topology changes among different phases and the difficulty in implementing the boundary conditions on the irregular solid surface. In this work, we first developed a diffuse-domain (DD) based phase-field model for multiphase flows in complex geometries. In this model, the irregular fluid region is embedded into a larger and regular domain by introducing a smooth characteristic function. Then, the reduction-consistent and conservative phase-field equation for the multiphase field and the consistent and conservative Navier-Stokes equations for the flow field are reformulated as the diffuse-domain based consistent and conservative (DD-CC) equations where some additional source terms are added to reflect the effects of boundary conditions. In this case, there is no need to directly treat the complex boundary conditions on the irregular solid surface, and additionally, based on a matched asymptotic analysis, it is also shown that the DD-CC equations can converge to the original governing equations as the interface width parameter tends to zero. Furthermore, to solve the DD-CC equations, we proposed a novel and simple lattice Boltzmann (LB) method with a Hermite-moment-based collision matrix which can not only keep consistent and conservation properties, but also improve the numerical stability with a flexible parameter. With the help of the direct Taylor expansion, the macroscopic DD-CC equations can be recovered correctly from the present LB method. Finally, to test the capacity of LB method, several benchmarks and complex problems are considered, and the numerical results show that the present LB method is accurate and efficient for the multiphase flows in complex geomerties.

physics.comp-ph↗
arXiv2023

A thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows

In this work, a thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows is proposed. In this model, a novel free energy for the gas-liquid-solid multiphase flows is established according to a ternary phase-field model, and it not only contains the standard bulk and interface free energies for two-phase flows, but also includes some additional terms to reflect the penalty in the solid phase and the wettability on the solid surface. Furthermore, a smooth indicator function of the solid phase is also introduced in the consistent Navier-Stokes equations to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface. Based on the proposed diffuse-interface model, the fluid interface dynamics, the fluid-structure interaction, and the wetting property of the solid surface can be described simply and efficiently. Additionally, the total energy is also proved to be dissipative for the two-phase flows in the stationary geometries. To test the present diffuse-interface model, we develop a consistent and conservative lattice Boltzmann method and conduct some simulations. The numerical results also confirm the energy dissipation and good capability of the proposed diffuse-interface model in the study of two-phase flows in complex geometries and gas-liquid-particle multiphase flows.

physics.flu-dyn↗
arXiv2023

A ternary phase-field model for two-phase flows in complex geometries

In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn-Hilliard model is considered as the solid phase, and only one Cahn-Hilliard equation with degenerate mobility needs to be solved due to the condition of volume conservation, which is consistent with the standard phase-field model with a single-scalar variable for two-phase flows. To depict different wetting properties at the complex fluid-solid boundaries, the spreading parameters in ternary phase-field model are determined based on the Young's law, in which the liquid-solid surface tension coefficient is assumed to be a linear function of gas-liquid surface tension coefficient and related to the contact angle and the minimum curvature of the solid surface. In addition, to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface, the phase-field variable of the solid phase is also used to derive the modified Navier-Stokes equations. To test the present model, we further develop a consistent and conservative Hermite-moment based lattice Boltzmann method where an adjustable scale factor is introduced to improve the numerical stability, and conduct the numerical simulations of several benchmark problems. The results illustrate that present model has the good capability in the study of the two-phase flows in complex geometries.

physics.flu-dyn↗
arXiv2023

A Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann model for the coupled Burgers' equations

In this work, a Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for d-dimensional coupled Burgers' equations is developed. We first adopt the Cole-Hopf transformation where an intermediate variable θis introduced to eliminate the nonlinear convection terms in the Burgers' equations on the velocity u=(u_1,u_2,...,u_d). In this case, a diffusion equation on the variable θcan be obtained, and particularly, the velocity u in the coupled Burgers' equations is determined by the variable θand its gradient term \nablaθ. Then we develop a general MRT-LB model with the natural moments for the d-dimensional transformed diffusion equation and present the corresponding macroscopic finite-difference scheme. At the diffusive scaling, the fourth-order modified equation of the developed MRT-LB model is derived through the Maxwell iteration method. With the aid of the free parameters in the MRT-LB model, we find that not only the consistent fourth-order modified equation can be obtained, but also the gradient term $\nablaθ$ can be calculated locally by the non-equilibrium distribution function with a fourth-order accuracy, this indicates that theoretically, the MRT-LB model for $d$-dimensional coupled Burgers' equations can achieve a fourth-order accuracy in space. Finally, some simulations are conducted to test the MRT-LB model, and the numerical results show that the proposed MRT-LB model has a fourth-order convergence rate, which is consistent with our theoretical analysis.

math.NA↗
arXiv2023

The macroscopic finite-difference scheme and modified equations of the general propagation multiple-relaxation-time lattice Boltzmann model

In this paper, we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations (MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation (NACDE) and Navier-Stokes equations (NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, two benchmark problems, Gauss hill problem and Poiseuille flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results are not only in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis.

math.NA↗
arXiv2023

A general fourth-order mesoscopic multiple-relaxation-time lattice Boltzmann model and equivalent macroscopic finite-difference scheme for two-dimensional diffusion equations

In this work, we first develop a general mesoscopic multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation with the constant diffusion coefficient and source term, where the D2Q5 (five discrete velocities in two-dimensional space) lattice structure is considered. Then we exactly derive the equivalent macroscopic finite-difference scheme of the MRT-LB model. Additionally, we also propose a proper MRT-LB model for the diffusion equation with a linear source term, and obtain an equivalent macroscopic six-level finite-difference scheme. After that, we conduct the accuracy and stability analysis of the finite-difference scheme and the mesoscopic MRT-LB model. It is found that at the diffusive scaling, both of them can achieve a fourth-order accuracy in space based on the Taylor expansion. The stability analysis also shows that they are both unconditionally stable. Finally, some numerical experiments are conducted, and the numerical results are also consistent with our theoretical analysis.

math.NA↗
arXiv2023

Divide and Adapt: Active Domain Adaptation via Customized Learning

Active domain adaptation (ADA) aims to improve the model adaptation performance by incorporating active learning (AL) techniques to label a maximally-informative subset of target samples. Conventional AL methods do not consider the existence of domain shift, and hence, fail to identify the truly valuable samples in the context of domain adaptation. To accommodate active learning and domain adaption, the two naturally different tasks, in a collaborative framework, we advocate that a customized learning strategy for the target data is the key to the success of ADA solutions. We present Divide-and-Adapt (DiaNA), a new ADA framework that partitions the target instances into four categories with stratified transferable properties. With a novel data subdivision protocol based on uncertainty and domainness, DiaNA can accurately recognize the most gainful samples. While sending the informative instances for annotation, DiaNA employs tailored learning strategies for the remaining categories. Furthermore, we propose an informativeness score that unifies the data partitioning criteria. This enables the use of a Gaussian mixture model (GMM) to automatically sample unlabeled data into the proposed four categories. Thanks to the "divideand-adapt" spirit, DiaNA can handle data with large variations of domain gap. In addition, we show that DiaNA can generalize to different domain adaptation settings, such as unsupervised domain adaptation (UDA), semi-supervised domain adaptation (SSDA), source-free domain adaptation (SFDA), etc.

cs.CV↗
arXiv2023

Exploration and Exploitation of Unlabeled Data for Open-Set Semi-Supervised Learning

In this paper, we address a complex but practical scenario in semi-supervised learning (SSL) named open-set SSL, where unlabeled data contain both in-distribution (ID) and out-of-distribution (OOD) samples. Unlike previous methods that only consider ID samples to be useful and aim to filter out OOD ones completely during training, we argue that the exploration and exploitation of both ID and OOD samples can benefit SSL. To support our claim, i) we propose a prototype-based clustering and identification algorithm that explores the inherent similarity and difference among samples at feature level and effectively cluster them around several predefined ID and OOD prototypes, thereby enhancing feature learning and facilitating ID/OOD identification; ii) we propose an importance-based sampling method that exploits the difference in importance of each ID and OOD sample to SSL, thereby reducing the sampling bias and improving the training. Our proposed method achieves state-of-the-art in several challenging benchmarks, and improves upon existing SSL methods even when ID samples are totally absent in unlabeled data.

cs.CV↗
arXiv2023

Multiple-distribution-function finite-difference lattice Boltzmann method for incompressible Navier-Stokes equation

In this paper, a multiple-distribution-function finite-difference lattice Boltzmann method (MDF-FDLBM) is proposed for the convection-diffusion system based incompressible Navier-Stokes equations (NSEs). By Chapman Enskog analysis, the convection-diffusion system based incompressible NSEs can be recovered from MDF-FDLBM. Some quantities, including the velocity gradient, velocity divergence, strain rate tensor, shear stress and vorticity, can be computed locally by the first-order moment of the non-equilibrium distribution function. Through the von Neumann analysis, we conduct the stability analysis for the MDF-FDLBM and incompressible finite-difference lattice Boltzmann method (IFDLBM). It is found that the IFDLBM will be more stable than that of MDF-FDLBM with small kinematic viscosity, and the MDF-FDLBM will be more stable than that of IFDLBM with large Courant-Friedrichs-Lewy condition number. Finally, some simulations are conducted to validate the MDF-FDLBM. The results agree well with the analytical solutions and previous results. Through the numerical testing, we find that the MDF-FDLBM has a second-order convergence rate in space and time. The MDF-FDLBMcombined with non-uniform grid also works well. Meanwhile, compared with IFDLBM, it can be found that MDF-FDLBM offers higher accuracy and computational efficiency, reducing computation time by more than 36%.

physics.flu-dyn↗
arXiv2023

Numerical Simulation of Power-Law Fluid Flow in a Trapezoidal Cavity using the Incompressible Finite-Difference Lattice Boltzmann Method

In this paper, a numerical investigation of power-law fluid flow in the trapezoidal cavity has been conducted by incompressible finite-difference lattice Boltzmann method (IFDLBM). By designing the equilibrium distribution function, the Navier-Stokes equations (NSEs) can be recovered exactly. Through the coordinate transformation method, the body-fitted grid in physical region is transformed into a uniform grid in computational region. The effect of Reynolds (Re) number, the power-law index $n$ and the vertical angle θ on the trapezoidal cavity are investigated. According to the numerical results, we come to some conclusions. For low Re number Re=100, it can be found that the behavior of power-law fluid flow becomes more complicated with the increase of n. And as vertical angle θ decreases, the flow becomes smooth and the number of vortices decreases. For high Re numbers, the flow development becomes more complex, the number and strength of vortices increase. If the Reynolds number increases further, the power-law fluid will changes from steady flow to periodic flow and then to turbulent flow. For the steady flow, the lager the θ, the more complicated the vortices. And the critical Re number from steady to periodic state decreases with the decrease of power-law index n.

physics.flu-dyn↗
arXiv2023

A comparative study of two Allen-Cahn models for immiscible $N$-phase flows by using a consistent and conservative lattice Boltzmann method

In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [\emph{Model A}: Zheng \emph{et al.}, Phys. Rev. E 101, 0433202 (2020) and \emph{Model B}: Mirjalili and Mani, (2023)] for the immiscible $N$-phase flows. Mathematically, these two AC equations can be proved to be equivalent under some approximate conditions. However, the effects of these approximations are unclear from the theoretical point of view, and would be considered numerically. To this end, we propose a consistent and conservative lattice Boltzmann method for the AC models for $N$-phase flows, and present some numerical comparisons of accuracy and stability between these two AC models. The results show that both two AC models have good performances in accuracy, but the \emph{Model B} is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the \emph{Model A}.

physics.flu-dyn↗
arXiv2023

Towards Accurate Post-Training Quantization for Vision Transformer

Vision transformer emerges as a potential architecture for vision tasks. However, the intense computation and non-negligible delay hinder its application in the real world. As a widespread model compression technique, existing post-training quantization methods still cause severe performance drops. We find the main reasons lie in (1) the existing calibration metric is inaccurate in measuring the quantization influence for extremely low-bit representation, and (2) the existing quantization paradigm is unfriendly to the power-law distribution of Softmax. Based on these observations, we propose a novel Accurate Post-training Quantization framework for Vision Transformer, namely APQ-ViT. We first present a unified Bottom-elimination Blockwise Calibration scheme to optimize the calibration metric to perceive the overall quantization disturbance in a blockwise manner and prioritize the crucial quantization errors that influence more on the final output. Then, we design a Matthew-effect Preserving Quantization for Softmax to maintain the power-law character and keep the function of the attention mechanism. Comprehensive experiments on large-scale classification and detection datasets demonstrate that our APQ-ViT surpasses the existing post-training quantization methods by convincing margins, especially in lower bit-width settings (e.g., averagely up to 5.17% improvement for classification and 24.43% for detection on W4A4). We also highlight that APQ-ViT enjoys versatility and works well on diverse transformer variants.

cs.CV↗
arXiv2022

The optimal displacement of immiscible two-phase fluids in a pore doublet

The displacement of multiphase fluid flow in a pore doublet is a fundamental problem, and is also of importance in understanding of the transport mechanisms of multiphase flows in the porous media. During the displacement of immiscible two-phase fluids in the pore doublet, the transport process is not only influenced by the capillary and viscous forces, but also affected by the channel geometry. In this paper, we first present a mathematical model to describe the two-phase fluid displacement in the pore doublet where the effects of capillary force, viscous force and the geometric structure are included. Then we derive an analytical solution of the model for the first time, and find that the displacement process is dominated by the capillary number, the viscosity ratio and the radius ratio. Furthermore, we define the optimal displacement that the wetting fluids in two daughter channels break through the branches simultaneously (both of them have the same breakthrough time), and also obtain the critical capillary number corresponding to the optimal displacement, which is related to the radius ratio of two daughter channels and viscosity ratio of two immiscible fluids. Finally, it is worthy noting that the present analytical results on the displacement in the pore doublet can be used to explain and understand the phenomenon of preferential imbibition or preferential flow in porous media.

physics.flu-dyn↗
arXiv2022

A diffuse-interface lattice Boltzmann method for the dendritic growth with thermosolutal convection

In this work, we proposed a diffuse interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter governed by the phase-field equation for the dendritic growth. The governing equations for solute and heat transfer are modified such that the previous special treatments for source term can be avoided. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are developed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, to test the present diffuse-interface LB method, we performed some simulations of the dendritic growth, and found that the numerical results are in good agreements with some previous works.

physics.flu-dyn↗
arXiv2022

Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues

In this paper, we develop a general rectangular multiple-relaxation-time lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equation (NCDE) by extending our recent unified framework of MRT-LB method [Z.H. Chai and B.C. Shi, Phys. Rev. E 102, 023306 (2020)], where a rectangular equilibrium distribution function (REDF) [J.H. Lu et al, Phil. Trans. R. Soc. A 369, 2311-2319 (2011)] on a rectangular lattice is utilized. Due to the anisotropy of discrete velocities on a rectangular lattice, the third-order moment of REDF is inconsistent with that of popular LB method, and thus the previous unified framework of MRT-LB method cannot be directly applied to the NSEs using the REDF on the rectangular rDdQq lattice. The macroscopic NSEs can be recovered from the RMRT-LB method through the direct Taylor expansion method by properly selecting the relaxation sub-matrix $\mathbf{S}_2$ which is related to kinetic viscosity and bulk viscosity. While the rectangular lattice does not lead to the change of the zero-th, first and second-order moments of REDF, thus the unified framework of MRT-LB method can be directly applied to the NCDE. It should be noted that the RMRT-LB model for NSEs can be derived on the rDdQq lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, and the RMRT-LB versions (if existed) of the previous MRT-LB models can be obtained, including those based on raw (natural)-moment, central-moment, Hermite-moment, and central Hermite-moment, respectively.

physics.comp-ph↗
arXiv2022

Compressing Models with Few Samples: Mimicking then Replacing

Few-sample compression aims to compress a big redundant model into a small compact one with only few samples. If we fine-tune models with these limited few samples directly, models will be vulnerable to overfit and learn almost nothing. Hence, previous methods optimize the compressed model layer-by-layer and try to make every layer have the same outputs as the corresponding layer in the teacher model, which is cumbersome. In this paper, we propose a new framework named Mimicking then Replacing (MiR) for few-sample compression, which firstly urges the pruned model to output the same features as the teacher's in the penultimate layer, and then replaces teacher's layers before penultimate with a well-tuned compact one. Unlike previous layer-wise reconstruction methods, our MiR optimizes the entire network holistically, which is not only simple and effective, but also unsupervised and general. MiR outperforms previous methods with large margins. Codes will be available soon.

cs.LG↗
arXiv2021

Contrastive Attention Network with Dense Field Estimation for Face Completion

Most modern face completion approaches adopt an autoencoder or its variants to restore missing regions in face images. Encoders are often utilized to learn powerful representations that play an important role in meeting the challenges of sophisticated learning tasks. Specifically, various kinds of masks are often presented in face images in the wild, forming complex patterns, especially in this hard period of COVID-19. It's difficult for encoders to capture such powerful representations under this complex situation. To address this challenge, we propose a self-supervised Siamese inference network to improve the generalization and robustness of encoders. It can encode contextual semantics from full-resolution images and obtain more discriminative representations. To deal with geometric variations of face images, a dense correspondence field is integrated into the network. We further propose a multi-scale decoder with a novel dual attention fusion module (DAF), which can combine the restored and known regions in an adaptive manner. This multi-scale architecture is beneficial for the decoder to utilize discriminative representations learned from encoders into images. Extensive experiments clearly demonstrate that the proposed approach not only achieves more appealing results compared with state-of-the-art methods but also improves the performance of masked face recognition dramatically.

cs.CV↗
arXiv2021

Consistent and conservative phase-field based lattice Boltzmann method for incompressible two-phase flows

In this work, we consider a general consistent and conservative phase-field model for the incompressible two-phase flows. In this model, not only the Cahn-Hilliard or Allen-Cahn equation can be adopted, but also the mass and the momentum fluxes in the Navier-Stokes equations are reformulated such that the consistency of reduction, consistency of mass and momentum transport, and the consistency of mass conservation are satisfied. We further develop a lattice Boltzmann (LB) method and show that through the direct Taylor expansion, the present LB method can correctly recover the consistent and conservative phase-field model. Additionally, if the divergence of the extra momentum flux is seen as a force term, the extra force in the present LB method would include another term which has not been considered in the previous LB models. To quantitatively evaluate the incompressibility and the consistency of the mass conservation, two statistical variables are introduced in the study of the deformation of a square droplet, and the results show that the present LB method is more accurate. The layered Poiseuille flow and a droplet spreading on an ideal wall are further investigated, and the numerical results are in good agreement with the analytical solutions. Finally, the problems of the Rayleigh-Taylor instability and dam break with the high Reynolds numbers and/or large density ratios are studied, and it is found that the present consistent and conservative LB method is robust for such complex two-phase flows.

physics.flu-dyn↗