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

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arXiv 2023年

作者： Chen, Xinmeng Chai, Zhenhua Zhao, Yong Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Statistics Changsha University of Science and Technology Hunan Changsha410114 China

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%. © 2023, CC BY.

关键词： Distribution functions

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

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arXiv 2023年

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. © 2023, CC BY.

关键词： Reynolds number

Breaking Barriers in Physical-World Adversarial Examples: Improving Robustness and Transferability via Robust Feature

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arXiv 2024年

作者： Wang, Yichen Chou, Yuxuan Zhou, Ziqi Zhang, Hangtao Wan, Wei Hu, Shengshan Li, Minghui National Engineering Research Center for Big Data Technology and System China Services Computing Technology and System Lab China Cluster and Grid Computing Lab China Hubei Engineering Research Center on Big Data Security China Hubei Key Laboratory of Distributed System Security China School of Cyber Science and Engineering Huazhong University of Science and Technology China School of Computer Science and Technology Huazhong University of Science and Technology China School of School of Software Engineering Huazhong University of Science and Technology China

As deep neural networks (DNNs) are widely applied in the physical world, many researches are focusing on physical-world adversarial examples (PAEs), which introduce perturbations to inputs and cause the model’s incorrect outputs. However, existing PAEs face two challenges: unsatisfactory attack performance (i.e., poor transferability and insufficient robustness to environment conditions), and difficulty in balancing attack effectiveness with stealthiness, where better attack effectiveness often makes PAEs more perceptible. In this paper, we explore a novel perturbation-based method to overcome the challenges. For the first challenge, we introduce a strategy Deceptive RF injection based on robust features (RFs) that are predictive, robust to perturbations, and consistent across different models. Specifically, it improves the transferability and robustness of PAEs by covering RFs of other classes onto the predictive features in clean images. For the second challenge, we introduce another strategy Adversarial Semantic Pattern Minimization, which removes most perturbations and retains only essential adversarial patterns in AEs. Based on the two strategies, we design our method Robust Feature Coverage Attack (RFCoA), comprising Robust Feature Disentanglement and Adversarial Feature Fusion. In the first stage, we extract target class RFs in feature space. In the second stage, we use attention-based feature fusion to overlay these RFs onto predictive features of clean images and remove unnecessary perturbations. Experiments show our method’s superior transferability, robustness, and stealthiness compared to existing state-of-the-art methods. Additionally, our method’s effectiveness can extend to Large Vision-Language Models (LVLMs), indicating its potential applicability to more complex tasks. Copyright © 2024, The Authors. All rights reserved.

关键词： Deep neural networks

ASYMPTOTIC BEHAVIOR OF THE PRINCIPAL EIGENVALUE OF A LINEAR SECOND ORDER ELLIPTIC OPERATOR WITH LARGE ADVECTION AND GENERAL BOUNDARY CONDITIONS

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arXiv 2023年

作者： Peng, Rui Zhang, Guanghui Zhou, Maolin School of Mathematical Sciences Zhejiang Normal University Zhejiang Jinhua321004 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Chern Institute of Mathematics and LPMC Nankai University Tianjin300071 China

Consider the eigenvalue problem of a linear second order elliptic operator: − D∆ − 2α∇m(x) · ∇ + V (x) = λ in Ω, complemented by the Dirichlet boundary condition or the following general Robin boundary condition: (Formula Presented) is a bounded smooth domain, n(x) is the unit exterior normal to ∂Ω at x ∈ ∂Ω, D > 0 and α > 0 are, respectively, the diffusion and advection coefficients, m ∈ C2(Ω), V ∈ C(Ω), β ∈ C(∂Ω) are given functions, and β allows to be positive, sign-changing or negative. In [41], the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as D → 0 or D → ∞ was studied. In this paper, when N ≥ 2, under proper conditions on the advection function m, we establish the asymptotic behavior of the principal eigenvalue as α → ∞, and when N = 1, we obtain a complete characterization for such asymptotic behavior provided m0 changes sign at most finitely many times. Our results complement or improve those in [4, 7, 44] and also partially answer some questions raised in [4]. © 2023, CC0.

关键词： Advection

Asymptotic Behavior of the Principal Eigenvalue of a Linear Second Order Elliptic Operator with Large Advection and General Boundary Conditions

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SSRN

SSRN 2023年

In this paper, we consider asymptotic behavior of the principal eigenvalue of some second order elliptic operator with general boundary conditions. For $N=1$, we provide a complete characterization of the asymptotic behavior, assuming that $m'$ changes sign at most finitely many times. Our findings not only improve upon the previous work in \cite{BHN2005,CL2008,PZ2018}, but also partially address some of the open questions posed in \cite{BHN2005}. Furthermore, our results elucidate the novel influence of boundary conditions on such asymptotics. To achieve these results, we develop several sophisticated techniques to overcome the new difficulties posed by the problems under consideration. © 2023, The Authors. All rights reserved.

关键词： Advection

NumbOD: A Spatial-Frequency Fusion Attack Against Object Detectors

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arXiv 2024年

作者： Zhou, Ziqi Li, Bowen Song, Yufei Yu, Zhifei Hu, Shengshan Wan, Wei Zhang, Leo Yu Yao, Dezhong Jin, Hai National Engineering Research Center for Big Data Technology and System China Services Computing Technology and System Lab China Cluster and Grid Computing Lab Hubei Engineering Research Center on Big Data Security China Hubei Key Laboratory of Distributed System Security China School of Computer Science and Technology Huazhong University of Science and Technology China School of Cyber Science and Engineering Huazhong University of Science and Technology China School of Information and Communication Technology Griffith University Australia

With the advancement of deep learning, object detectors (ODs) with various architectures have achieved significant success in complex scenarios like autonomous driving. Previous adversarial attacks against ODs have been focused on designing customized attacks targeting their specific structures (e.g., NMS and RPN), yielding some results but simultaneously constraining their scalability. Moreover, most efforts against ODs stem from image-level attacks originally designed for classification tasks, resulting in redundant computations and disturbances in object-irrelevant areas (e.g., background). Consequently, how to design a model-agnostic efficient attack to comprehensively evaluate the vulnerabilities of ODs remains challenging and unresolved. In this paper, we propose NumbOD, a brand-new spatial-frequency fusion attack against various ODs, aimed at disrupting object detection within images. We directly leverage the features output by the OD without relying on its internal structures to craft adversarial examples. Specifically, we first design a dual-track attack target selection strategy to select high-quality bounding boxes from OD outputs for targeting. Subsequently, we employ directional perturbations to shift and compress predicted boxes and change classification results to deceive ODs. Additionally, we focus on manipulating the high-frequency components of images to confuse ODs' attention on critical objects, thereby enhancing the attack efficiency. Our extensive experiments on nine ODs and two datasets show that NumbOD achieves powerful attack performance and high stealthiness. Copyright © 2024, The Authors. All rights reserved.

关键词： Object detection

DarkSAM: Fooling Segment Anything Model to Segment Nothing

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arXiv 2024年

作者： Zhou, Ziqi Song, Yufei Li, Minghui Hu, Shengshan Wang, Xianlong Zhang, Leo Yu Yao, Dezhong Jin, Hai National Engineering Research Center for Big Data Technology and System China Services Computing Technology and System Lab China Cluster and Grid Computing Lab China Hubei Engineering Research Center on Big Data Security China Hubei Key Laboratory of Distributed System Security China School of Cyber Science and Engineering Huazhong University of Science and Technology China School of Software Engineering Huazhong University of Science and Technology China School of Information and Communication Technology Griffith University Australia

Segment Anything Model (SAM) has recently gained much attention for its outstanding generalization to unseen data and tasks. Despite its promising prospect, the vulnerabilities of SAM, especially to universal adversarial perturbation (UAP) have not been thoroughly investigated yet. In this paper, we propose DarkSAM, the first prompt-free universal attack framework against SAM, including a semantic decoupling-based spatial attack and a texture distortion-based frequency attack. We first divide the output of SAM into foreground and background. Then, we design a shadow target strategy to obtain the semantic blueprint of the image as the attack target. DarkSAM is dedicated to fooling SAM by extracting and destroying crucial object features from images in both spatial and frequency domains. In the spatial domain, we disrupt the semantics of both the foreground and background in the image to confuse SAM. In the frequency domain, we further enhance the attack effectiveness by distorting the high-frequency components (i.e., texture information) of the image. Consequently, with a single UAP, DarkSAM renders SAM incapable of segmenting objects across diverse images with varying prompts. Experimental results on four datasets for SAM and its two variant models demonstrate the powerful attack capability and transferability of DarkSAM. Our codes are available at: https://***/CGCL-codes/DarkSAM. Copyright © 2024, The Authors. All rights reserved.

关键词： Frequency domain analysis

A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media

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Procedia Computer science 2016年 80卷 1324-1333页

作者： Huangxin Chen Shuyu Sun School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian 361005 China and King Abdullah University of Science and Technology (KAUST) Physical Science and Engineering Division (PSE) Thuwal 23955-6900 Saudi Arabia King Abdullah University of Science and Technology (KAUST) Physical Science and Engineering Division (PSE) Thuwal 23955-6900 Saudi Arabia

In this paper, we develop a two-scale reduced model for simulating the Darcy flow in two- dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved on unstructured grid which represents the fractures accurately, while in the EFM used on the coarse scale, the flux interaction between fractures and matrix are dealt with as a source term, and the matrix-fracture system can be resolved on structured grid. The Raviart-Thomas mixed finite element methods are used for the solution of the coupled flows in the matrix and the fractures on both fine and coarse scales. Numerical results are presented to demonstrate the efficiency of the proposed model for simulation of flow in fractured porous media.

关键词： Fractured porous media two-scale discrete fracture model embedded fracture model mixed finite element method

A computationally-efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

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arXiv 2020年

作者： Ding, Yuemin Liu, Jin-Long Li, Xiaohui Tian, Yu-Chu Yu, Zu-Guo School of Computer Science and Engineering Tianjin University of Technology Tianjin300384 China School of Computer Science Queensland University of Technology BrisbaneQLD4000 Australia Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China School of Information Science and Engineering Wuhan University of Science and Technology Wuhan Hubei430081 China

The fractality of complex networks has attracted much attention with extensive investigations over the last 15 years. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful tool to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. One of the widely used methods for fractal analysis is box-covering. It uses the minimum number of covering boxes to calculate the fractal dimension of complex networks, and is known to be NP-hard. More severely, in comparison with fractal analysis algorithms, MFA algorithms have much higher computational complexity. Among various MFA algorithms for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive. Thus, so far it has only been applied to small-scale complex networks of the size of about tens of thousands of nodes. It becomes challenging to implement the MFA for large-scale networks with tens of millions of nodes. It is also not clear whether or not MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally-efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of complex networks, our CESA employs the breadth-first search (BFS) technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. Our CESA's input is a sparse data structure derived from the compressed sparse row (CSR) format designed for compressed storage of the adjacency matrix of large-scale network. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic

关键词： Computational efficiency