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Physical Review E 2019年第6期99卷 063316-063316页

作者： Xiuya Guo Zhenhua Chai Shengyong Pang Yong Zhao Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Material Processing and Die & Mould Technology Huazhong University of Science and Technology Wuhan 430074 China

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.

关键词： Lattice-Boltzmann methods

Efficient Numerical Computation of Time-Fractional Nonlinear Schrodinger Equations in Unbounded Domain

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Communications in Computational Physics 2019年第1期25卷 218-243页

作者： Jiwei Zhang Dongfang Li Xavier Antoine Beijing Computational Science Research Center Beijing 100193P.R.China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Institut Elie Cartan de Lorraine UMR CNRS 7502Universit́e de LorraineInria Nancy-Grand EstSPHINX TeamF-54506 Vandoeuvre-l`es-Nancy CedexFrance

The aim of this paper is to derive a stable and efficient scheme for solving the one-dimensional time-fractional nonlinear Schrodinger equation set in an unbounded *** first derive absorbing boundary conditions for the fractional system by using the unified approach introduced in[47,48]and a linearization ***,the initial boundary-value problem for the fractional system with ABCs is discretized,a stability analysis is developed and the error estimate O(h^(2)+τ)is *** accel-erate the L1-scheme in time,a sum-of-exponentials approximation is introduced to speed-up the evaluation of the Caputo fractional *** resulting algorithm is highly efficient for long time ***,we end the paper by reporting some numerical simulations to validate the properties(accuracy and efficiency)of the derived scheme.

关键词： Time-fractional nonlinear Schrodinger equation absorbing boundary condition sta-bility analysis convergence analysis sum-of-exponentials approximation

A block triple-relaxation-Time lattice Boltzmann model for nonlinear anisotropic convection-diffusion equations

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arXiv 2019年

作者： Zhao, Yong Wu, Yao Chai, Zhenhua Shi, Baochang Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China

A block triple-relaxation-Time (B-TriRT) lattice Boltzmannmodel for general nonlinear anisotropic convection-diffusion equations (NACDEs) is proposed, and the Chapman-Enskog analysis shows that the present B-TriRT model can recover the NACDEs correctly. There are some striking features of the present B-TriRT model: firstly, the relaxation matrix of B-TriRT model is partitioned into three relaxation parameter blocks, rather than a diagonal matrix in general multiple-relaxation-Time (MRT) model;secondly, based on the analysis of half-way bounce-back (HBB) scheme for Dirichlet boundary conditions, we obtain an expression to determine the relaxation parameters;thirdly, the anisotropic diffusion tensor can be recovered by the relaxation parameter block that corresponds to the first-order moment of nonequilibriumdistribution function. A number of simulations of isotropic and anisotropic convection-diffusion equations are conducted to validate the present B-TriRT model. The results indicate that the present model has a second-order accuracy in space, and is also more accurate and more stable than some available lattice Boltzmann models. Copyright © 2019, The Authors. All rights reserved.

关键词： Diffusion in liquids

Discrete effects on some boundary schemes of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations

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arXiv 2019年

作者： Wu, Yao Zhao, Yong Chai, Zhenhua Shi, Baochang 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, we perform a more general analysis on the discrete effects of some boundary schemes of the popular one- to three-dimensional DnQq multiple-relaxation-time lattice Boltzmann model for convection-diffusion equation (CDE). Investigated boundary schemes include anti-bounce-back(ABB) boundary scheme, bounce-back(BB) boundary scheme and non-equilibrium extrapolation(NEE) boundary scheme. In the analysis, we adopt a transform matrix M constructed by natural moments in the evolution equation, and the result of ABB boundary scheme is consistent with the existing work of orthogonal matrix M. We also find that the discrete effect does not rely on the choice of transform matrix, and obtain a relation to determine some of the relaxation-time parameters which can be used to eliminate the numerical slip completely under some assumptions. In this relation, the weight coefficient is considered as an adjustable parameter which makes the parameter adjustment more flexible. The relaxation factors associated with second moments can be used to eliminate the numerical slip of ABB boundary scheme and BB boundary scheme while the numerical slip can not be eliminated of NEE boundary scheme. Furthermore, we extend the relations to complex-valued CDE, several numerical examples are used to test the relations. Copyright © 2019, The Authors. All rights reserved.

关键词： Diffusion in liquids

Generalized lattice boltzmann method: modeling, analysis, and elements

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arXiv 2019年

作者： Shi, Baochang Chai, Zhenhua 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, we first present a unified framework for the modelling of generalized lattice Boltzmann method (GLBM). We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansion and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes equations and nonlinear convection-diffusion equations from the GLBM, and show that from mathematical point of view, these four analysis methods are equivalent to each other. Finally, we give some elements that are needed in the implementation of the GLBM, and also find that some available LB models can be obtained from this GLBM. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear equations

Maxwell-Stefan-theory-based lattice Boltzmann model for diffusion in multicomponent mixtures

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Physical Review E 2019年第2期99卷 023312-023312页

作者： Zhenhua Chai Xiuya Guo Lei Wang Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Physics China University of Geosciences Wuhan 430074 China

The phenomena of diffusion in multicomponent (more than two components) mixtures are universal in both science and engineering, and from the mathematical point of view, they are usually described by the Maxwell-Stefan (MS)-theory-based diffusion equations where the molar average velocity is assumed to be zero. In this paper, we propose a multiple-relaxation-time lattice Boltzmann (LB) model for the mass diffusion in multicomponent mixtures and also perform a Chapman-Enskog analysis to show that the MS continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS-theory-based diffusion equations are just a diffusion type of partial differential equations, we can also adopt much simpler lattice structures to reduce the computational cost of present LB model. We then conduct some simulations to test this model and find that the results are in good agreement with the previous work. Besides, the reverse diffusion, osmotic diffusion, and diffusion barrier phenomena are also captured. Finally, compared to the kinetic-theory-based LB models for multicomponent gas diffusion, the present model does not include any complicated interpolations, and its collision process can still be implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model.

关键词： Lattice-Boltzmann methods

On Coupling Lemma and Stochastic Properties with Unbounded Observables for 1-d Expanding Maps

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arXiv 2020年

作者： Chen, Jianyu Zhang, Hong-Kun Zhang, Yiwei School of Mathematical Sciences Center for Dynamical Systems and Differential Equations Soochow University SuzhouJiangsu215006 China Department of Mathematics and Statistics University of Massachusetts Amherst AmherstMA01003 United States School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Hua-Zhong University of Sciences and Technology Wuhan430074 China

In this paper, we establish a coupling lemma for standard families in the setting of piecewise expanding interval maps with countably many branches. Our method merely requires that the expanding map satisfies Chernov’s one-step expansion at q-scale and eventually covers a magnet interval. Therefore, our approach is particularly powerful for maps whose inverse Jacobian has low regularity and those who does not satisfy the big image property. The main ingredients of our coupling method are two crucial lemmas: the growth lemma in terms of the characteristic Z function and the covering ratio lemma over the magnet interval. We first prove the existence of an absolutely continuous invariant measure. What is more important, we further show that the growth lemma enables the liftablity of the Lebesgue measure to the associated Hofbauer tower, and the resulting invariant measure on the tower admits a decomposition of Pesin-Sinai type. Furthermore, we obtain the exponential decay of correlations and the almost sure invariance principle (which is a functional version of the central limit theorem). For the first time, we are able to make a direct relation between the mixing rates and the Z function, see (2.7). The novelty of our results relies on establishing the regularity of invariant density, as well as verifying the stochastic properties for a large class of unbounded observables. Finally, we verify our assumptions for several well known examples that were previously studied in the literature, and unify results to these examples in our framework. Copyright © 2020, The Authors. All rights reserved.

关键词： Inverse problems

Corrigendum to ‘Comparative study of natural convection melting inside a cubic cavity using an improved two-relaxation-time lattice Boltzmann model’ [International Journal of Heat and Mass Transfer, 143 (2019) 118449]

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International Journal of Heat and Mass Transfer 2021年 166卷

作者： Yong Zhao Lei Wang Zhenhua Chai Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Physics China University of Geosciences Wuhan 430074 China

The Most Probable Transition Paths of Stochastic Dynamical Systems: A Sufficient and Necessary Characterization

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arXiv 2021年

作者： Huang, Yuanfei Huang, Qiao Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Statistics and Data Science National University of Singapore 6 Science Drive 2 Singapore117546 Singapore School of Data Science City University of Hong Kong Kowloon Hong Kong Department of Mathematics Faculty of Sciences University of Lisbon Campo Grande Edifício C6 LisboaPT-1749-016 Portugal Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 21 Nanyang Link Singapore637371 Singapore The Dongguan Key Laboratory for Data Science and Intelligent Medicine Department of Mathematics Department of Physics Great Bay University Guangdong Dongguan523000 China

The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager–Machlup action functional and can be described by a necessary but not sufficient condition, the Euler–Lagrange equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary characterization for the most probable transition paths of stochastic dynamical systems with Brownian noise. We prove that, under appropriate conditions, the most probable transition paths are completely determined by a first-order ordinary differential equation. The equivalence is established by showing that the Onsager–Machlup action functional of the original system can be derived from the corresponding Markovian bridge process. For linear stochastic systems and the nonlinear Hongler’s model, the first-order differential equations determining the most probable transition paths are shown analytically to imply the Euler–Lagrange equations of the Onsager–Machlup functional. For general nonlinear systems, the determining first-order differential equations can be approximated, in a short time or for the small noise case. Some numerical experiments are presented to illustrate our results. Copyright © 2021, The Authors. All rights reserved.

关键词： Dynamical systems

LOW MACH NUMBER LIMIT AND FAR FIELD CONVERGENCE RATES OF POTENTIAL FLOWS IN MULTI-DIMENSIONAL NOZZLES WITH AN OBSTACLE INSIDE

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arXiv 2020年

作者： Ma, Lei Wang, Tian-Yi Xie, Chunjing School of Mathematical Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China Department of Mathematics School of Science Wuhan University of Technology 122 Luoshi Road Wuhan Hubei430070 China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing and SHL-MAC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

This paper considers the low Mach number limit and far field convergence rates of steady Euler flows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First, the well-posedness theory for both incompressible and compressible subsonic flows with external forces in multidimensional nozzle with an obstacle inside are established by several uniform estimates. The uniformly subsonic compressible flows tend to the incompressible flows as quadratic order of Mach number as the compressibility parameter goes to zero. Furthermore, we also give the convergence rates of both incompressible flow and compressible flow at far fields as the boundary of nozzle goes to flat even when the forces do not admit convergence rate at far fields. The convergence rates obtained for the flows at far fields clearly describe the effects of the external force. Copyright © 2020, The Authors. All rights reserved.

关键词： Nozzles