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Multiple-distribution-function lattice Boltzmann method for convection-diffusion-system based incompressible Navier-Stokes equations

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arXiv 2021年

作者： Chai, Zhenhua Shi, Baochang Zhan, Chengjie 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

In this paper, a multiple-distribution-function lattice Boltzmann method (MDF-LBM) with multiple-relaxation-time model is proposed for incompressible Navier-Stokes equations (NSEs) which are considered as the coupled convection-diffusion equations (CDEs). Through direct Taylor expansion analysis, we show that the Navier-Stokes equations can be recovered correctly from the present MDF-LBM, and additionally, it is also found that the velocity and pressure can be directly computed through the zero and first-order moments of distribution function. Then in the framework of present MDF-LBM, we develop a locally computational scheme for the velocity gradient where the first-order moment of the non-equilibrium distribution is used, this scheme is also extended to calculate the velocity divergence, strain rate tensor, shear stress and vorticity. Finally, we also conduct some simulations to test the MDF-LBM, and find that the numerical results not only agree with some available analytical and numerical solutions, but also have a second-order convergence rate in space. © 2021, CC BY.

关键词： Kinetic theory

Analysis of error localization of Chebyshev spectral approximations

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arXiv 2021年

Chebyshev spectral methods are widely used in numerical computations. When the underlying function has a singularity, it has been observed by L. N. Trefethen in 2011 that its Chebyshev interpolants exhibit an error localization property, that is, their errors in a neighborhood of the singularity are obviously larger than elsewhere. In this paper, we first present a pointwise error analysis for Chebyshev projections of functions with a singularity and prove that the rate of convergence of Chebyshev projections of degree n at each point away from the singularity is one power of n faster than that of at the singularity. This gives a rigorous justification for the error localization of Chebyshev projections. We then extend the framework of our analysis to Chebyshev interpolants, Chebyshev spectral differentiations and Legendre projections and justify their error localization using similar arguments. As a result, we find that Chebyshev spectral differentiations converge faster than their best counterparts except in a neighborhood of the singularity and, in the particular case where the singularity is located in the interior of interval, they converge even faster than their best counterparts in the maximum *** Codes 41A10, 41A25, 41A50 © 2021, CC BY-NC-SA.

关键词： Numerical methods

Splitting Method for Stochastic Navier-Stokes Equations

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arXiv 2025年

作者： Zhu, Jie Zhu, Yujun Ming, Ju Gunzburger, Max D. School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Department of Scientific Computing Florida State University TallahasseeFL32304 United States

This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS component and a stochastic equation. We rigorously analyze the proposed splitting method from the perspectives of equivalence, stability, existence and uniqueness of the solution. We also propose a modified splitting scheme, which simplified the stochastic equation by omitting its nonlinear terms. A detailed analysis of the solution properties for this modified approach is provided. Additionally, we discuss the statistical errors with both the original splitting format and the modified scheme. Our theoretical and numerical studies demonstrate that the equivalent splitting scheme exhibits significantly enhanced stability compared to the original stochastic NS equations, enabling more effective handling of nonlinear characteristics. Several numerical experiments were performed to compare the statistical errors of the splitting method and the modified splitting method. Notably, the deterministic NS equation in the splitting method does not require repeated solving, and the stochastic equation in the modified scheme is free of nonlinear terms. These features make the modified splitting method particularly advantageous for large-scale computations, as it significantly improves computational efficiency without compromising accuracy. Copyright © 2025, The Authors. All rights reserved.

关键词： Navier Stokes equations

Convergence analysis of a finite difference method for stochastic Cahn-Hilliard equation

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arXiv 2022年

作者： Hong, Jialin Jin, Diancong Sheng, Derui LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

This paper presents the convergence analysis of the spatial finite difference method (FDM) for the stochastic Cahn–Hilliard equation with Lipschitz nonlinearity and multiplicative noise. Based on fine estimates of the discrete Green function, we prove that both the spatial semi-discrete numerical solution and its Malliavin derivative have strong convergence order 1. Further, by showing the negative moment estimates of the exact solution, we obtain that the density of the spatial semi-discrete numerical solution converges in L1(R) to the exact one. Finally, we apply an exponential Euler method to discretize the spatial semi-discrete numerical solution in time and show that the temporal strong convergence order is nearly 83, where a difficulty we overcome is to derive the optimal Hölder continuity of the spatial semi-discrete numerical solution. Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

DENSITY CONVERGENCE OF A FULLY DISCRETE FINITE DIFFERENCE METHOD FOR STOCHASTIC CAHN-HILLIARD EQUATION

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arXiv 2022年

This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn-Hilliard equation driven by multiplicative space-time white noises. The main difficulty lies in the control of the drift coefficient that is neither globally Lipschitz nor one-sided Lipschitz. To handle this difficulty, we propose a novel localization argument and derive the strong convergence rate of the numerical solution to estimate the total variation distance between the exact and numerical solutions. This along with the existence of the density of the numerical solution finally yields the convergence of density in L1() of the numerical solution. Our results partially answer positively to the open problem emerged in [J. Cui and J. Hong, J. Differential Equations (2020)] on computing the density of the exact solution numerically. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite difference method

GAUSSIAN QUADRATURE RULES FOR COMPOSITE HIGHLY OSCILLATORY INTEGRALS

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arXiv 2021年

作者： Wu, Menghan Wang, Haiyong School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory od Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

Highly oscillatory integrals of composite type arise in electronic engineering and their calculations are a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is constructed based on the classical theory of orthogonal polynomials and its nodes and weights can be computed efficiently by using tools of numerical linear algebra. An interesting connection between the quadrature nodes and the Legendre points is proved and it is shown that the rate of convergence of this rule depends solely on the regularity of the non-oscillatory part of the integrand. The second one is constructed with respect to a sign-changing function and the classical theory of Gaussian quadrature can not be used anymore. We explore theoretical properties of this Gaussian quadrature, including the trajectories of the quadrature nodes and the convergence rate of these nodes to the endpoints of the integration interval, and prove its asymptotic error estimate under suitable hypotheses. Numerical experiments are presented to demonstrate the performance of the proposed *** Codes 65D30 Copyright © 2021, The Authors. All rights reserved.

关键词： Computation theory

Denial-of-Service or Fine-Grained Control: Towards Flexible Model Poisoning Attacks on Federated Learning

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arXiv 2023年

作者： Zhang, Hangtao Yao, Zeming Zhang, Leo Yu Hu, Shengshan Chen, Chao Liew, Alan Li, Zhetao School of Cyber Science and Engineering Huazhong University of Science and Technology China Swinburne University of Technology Australia Griffith University Australia National Engineering Research Center for Big Data Technology and System China Services Computing Technology and System Lab. Hubei Key Laboratory of Distributed System Security China Hubei Engineering Research Center on Big Data Security China RMIT University Australia Xiangtan University China

Federated learning (FL) is vulnerable to poisoning attacks, where adversaries corrupt the global aggregation results and cause denial-of-service (DoS). Unlike recent model poisoning attacks that optimize the amplitude of malicious perturbations along certain prescribed directions to cause DoS, we propose a Flexible Model Poisoning Attack (FMPA) that can achieve versatile attack goals. We consider a practical threat scenario where no extra knowledge about the FL system (e.g., aggregation rules or updates on benign devices) is available to adversaries. FMPA exploits the global historical information to construct an estimator that predicts the next round of the global model as a benign reference. It then fine-tunes the reference model to obtain the desired poisoned model with low accuracy and small perturbations. Besides the goal of causing DoS, FMPA can be naturally extended to launch a fine-grained controllable attack, making it possible to precisely reduce the global accuracy. Armed with precise control, malicious FL service providers can gain advantages over their competitors without getting noticed, hence opening a new attack surface in FL other than DoS. Even for the purpose of DoS, experiments show that FMPA significantly decreases the global accuracy, outperforming six state-of-the-art attacks. © 2023, CC BY.

关键词： Federated learning

Securing Sdn/Nfv-Enabled Campus Networks with Software-Defined Perimeter-Based Zero-Trust Architecture

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SSRN

SSRN 2023年

作者： Ruambo, Francis A. Zou, Deqing Lopes, Ivandro O. Yuan, Bin School of Cyber Science and Engineering Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Distributed System Security Wuhan China Hubei Engineering Research Center on Big Data Security Wuhan China National Engineering Research Center for Big Data Technology and System Wuhan China Services Computing Technology and System Lab Wuhan China Cluster and Grid Computing Lab Wuhan China Mbeya university of Science and Technology Mbeya131 Tanzania United Republic of Nucleo Operacional para a Sociedade de Informacao Cape Verde Songshan Laboratory Zhengzhou China

Network softwarization is a breakthrough in designing modern networks and providing numerous new network operations and services. This change is exemplified by Software Defined Networks (SDN) and Network Function Virtualization (NFV). As a result, the combination of SDN and NFV (SDN/NFV) frameworks and individual SDN and NFV frameworks have gained substantial traction in network security over the past decade, significantly supporting on-demand protection measures. However, the inherent security shortcomings of SDN, NFV, and SDN/NFV frameworks provide the fundamental issue in implementing security procedures via network softwarization. To solve this issue, we present a Software-Defined Perimeter (SDP)-powered Zero-Trust Architecture (ZTA) to improve security in the SDN/NFV-enabled campus network holistically. In addition to this, we also propose a threat model and quantitatively assess the suggested approach's performance and security. Furthermore, we highlight potential zero-trust network security function implementations in SDN/NFV-enabled infrastructure to increase protection for endpoint devices, network resources, and flows for detecting threats and responding effectively with minimal latency and overhead. © 2023, The Authors. All rights reserved.

关键词： Access control

Research on the Evolution Mechanism of Friction Wear Based on Macroscopic Dynamics

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SSRN

SSRN 2024年

作者： Jia, Bowen Pei, Shixun Yang, Fangchao Li, Honggang Chen, Bingxue Zhao, Menghao Chen, Yuanhang Wang, Liang Hong, Wei MOE Key Laboratory of Fundamental Physical Quantities Measurement Hubei Key Laboratory of Gravitation and Quantum Physics PGMF School of Physics Huazhong University of Science and Technology Wuhan430074 China School of Aero-engine Engineering Zhengzhou University of Aeronautics Zhengzhou450046 China Intelligent Computing Hardware Center Zhejiang Lab Hangzhou311121 China CYG Sunri Co. Ltd. Shenzhen518057 China

This paper models the macroscopic dynamics of wear based on the linear damage mechanism, abstracting state variables of loss power, friction pair characteristics and debris characteristics. The wear evolution trend is then analyzed from system stability perspective by the Routh criterion. Furthermore, wear evolution mechanism is studied by Monte Carlo simulation within reasonable parameter ranges. Finally, the effects of multiple factors on wear evolution are analyzed by critical parameter perturbation. The results show that the action and correlation coefficients between the state variables would influence the evolution direction of friction wear. The reasonable combination of these parameters can effectively reduce loss power, decrease roughness and fluctuation of friction pairs, and slow growth rate of debris mass. © 2024, The Authors. All rights reserved.

关键词： Wear of materials