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Physical Review E 2021年第1期104卷 015312-015312页

作者： Yuxin Lin Ning Hong Baochang Shi Zhenhua Chai School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China School of General Education Wuchang University of Technology Wuhan 430223 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China

In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then through the theoretical analysis, we derive an explicit four-level finite-difference scheme from this MRT-LB model. The results show that the four-level finite-difference scheme is unconditionally stable, and through adjusting the weight coefficient ω0 and the relaxation parameters s1 and s2 corresponding to the first and second moments, it can also have a sixth-order accuracy in space. Finally, we also test the four-level finite-difference scheme through some numerical simulations and find that the numerical results are consistent with our theoretical analysis.

关键词： Lattice-Boltzmann methods

DISPERSIVE ESTIMATES FOR THE SCHRÖDINGER EQUATION WITH FINITE RANK PERTURBATIONS

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arXiv 2022年

作者： Cheng, Han Huang, Shanlin Zheng, Quan School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we investigate dispersive estimates for the time evolution of Hamiltonians (Equation presented) where each j satisfies certain smoothness and decay conditions. We show that, under a spectral assumption, there exists a constant C = C(N, d, 1,..., N) > 0 such that (Equation presented), for t > 0. As far as we are aware, this seems to provide the first study of L1 − L∞ estimates for finite rank perturbations of the Laplacian in any dimension. We first deal with rank one perturbations (N = 1). Then we turn to the general case. The new idea in our approach is to establish the Aronszajn-Krein type formula for finite rank perturbations. This allows us to reduce the analysis to the rank one case and solve the problem in a unified manner. Moreover, we show that in some specific situations, the constant C(N, d, 1,..., N) grows polynomially in N. Finally, as an application, we are able to extend the results to N = ∞ and deal with some trace class *** Codes 35J10, 81Q15, 42B37 Copyright © 2022, The Authors. All rights reserved.

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Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations

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Physical Review E 2020年第2期101卷 023306-023306页

作者： Jinlong Shang Zhenhua Chai Huili 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 Computer Science Wuhan Textile University Wuhan 430073 China

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for a general nonlinear convection-diffusion equation (NCDE) and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the present DUGKS through some classic convection-diffusion equations, and we find that the numerical results are in good agreement with analytical solutions and that the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, the DUGKS can also adopt the nonuniform mesh. Besides, we perform some comparisons among the DUGKS, the finite-volume lattice Boltzmann model (FV-LBM), the single-relaxation-time lattice Boltzmann model (SLBM), and the multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the present DUGKS is more accurate than the FV-LBM, more stable than the SLBM, and almost has the same accuracy as the MRT-LBM. Moreover, the use of nonuniform mesh may make the DUGKS model more flexible.

关键词： Lattice-Boltzmann methods

Improved phase-field-based lattice Boltzmann method for thermocapillary flow

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Physical Review E 2022年第1期105卷 015314-015314页

作者： Liqing Yue Zhenhua Chai Huili 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 Mathematical and Computer Sciences Wuhan Textile University Wuhan 430074 China

In this paper, we present an improved phase-field-based lattice Boltzmann (LB) method for thermocapillary flows with large density, viscosity, and thermal conductivity ratios. The present method uses three LB models to solve the conservative Allen-Cahn equation, the incompressible Navier-Stokes equations, and the temperature equation. To overcome the difficulty caused by the convection term in solving the convection-diffusion equation for the temperature field, we first rewrite the temperature equation as a diffuse equation where the convection term is regarded as the source term and then construct an improved LB model for the diffusion equation. The macroscopic governing equations can be recovered correctly from the present LB method; moreover, the present LB method is much simpler and more efficient. In order to test the accuracy of this LB method, several numerical examples are considered, including the planar thermal Poiseuille flow of two immiscible fluids, the two-phase thermocapillary flow in a nonuniformly heated channel, and the thermocapillary Marangoni flow of a deformable bubble. It is found that the numerical results obtained from the present LB method are consistent with the theoretical prediction and available numerical data, which indicates that the present LB method is an effective approach for the thermocapillary flows.

关键词： Drops & bubbles Multiphase flows Lattice-Boltzmann methods Navier-Stokes equation

Three-stage GA-LM algorithm for surface roughness parameters formula construction

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Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics 2015年第11期27卷 2192-2200页

作者： Liu, Xinru Liu, Shengjun Tang, Jinyuan Zhou, Wei Institute of Engineering Modeling and Scientific Computing School of Mathematics and Statistics Central South University Changsha410083 China State Key Laboratory of High Performance Complex Manufacturing Central South University Changsha410083 China

Based on the function approximation theory, the formulas for calculating surface roughness parameters are obtained by optimizing the coefficients of the function template. At first, a global approximate solution set is obtained by optimizing the initial function template using genetic algorithm. Then, the set is taken as the initial value of Levenberg-Marquardt (LM) algorithm to obtain the better local optimal solution set, and the two algorithms are used in turn until the solutions are convergent or the largest switching times are reached. At last, according to the convergence precision of the solutions and the value of each monomial, the growth or trim operation is conducted on the function template, and the two optimization algorithms are executed again;until the termination conditions are satisfied. The numerical simulation examples show the algorithm has the better ability to find the optimal solution and the good robustness. Moreover, the method is easy to carry out, and can be used in engineering practice. ©, 2015, Institute of computing Technology. All right reserved.

关键词： Genetic algorithms

How much faster does the best polynomial approximation converge than Legendre projection?

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arXiv 2020年

作者： Wang, Haiyong 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

We compare the convergence behavior of best polynomial approximations and Legendre and Chebyshev projections and derive optimal rates of convergence of Legendre projections for analytic and differentiable functions in the maximum norm. For analytic functions, we show that the best polynomial approximation of degree n is better than the Legendre projection of the same degree by a factor of n1/2. For differentiable functions such as piecewise analytic functions and functions of fractional smoothness, however, we show that the best approximation is better than the Legendre projection by only some constant factors. Our results provide some new insights into the approximation power of Legendre projections. Copyright © 2020, The Authors. All rights reserved.

关键词： Functions

Anisotropic spectral manifold wavelet descriptor for deformable shape analysis and matching 26

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Anisotropic spectral manifold wavelet descriptor for deforma...

26th Pacific Conference on Computer Graphics and Applications, Pacific Graphics 2018

作者： Li, Qinsong Liu, Shengjun Hu, Ling Liu, Xinru Institute of Engineering Modeling and Scientific Computing Central South University Hunan Changsha410083 China School of Mathematics and Computational Science Hunan First Normal University Hunan Changsha410205 China State Key Laboratory of High Performance Manufacturing Complex Central South University Hunan Changsha410083 China

ISBN: (纸本)9783038680734

In this paper, we present a novel framework termed Anisotropic Spectral Manifold Wavelet Transform (ASMWT) for shape analysis. ASMWT comprehensively analyzes the signals from multiple directions on local manifold regions of the shape with a series of low-pass and band-pass frequency filters in each direction. Using the ASMWT coefficients of a very simple function, we efficiently construct a localizable and discriminative multiscale point descriptor, named as the Anisotropic Spectral Manifold Wavelet Descriptor (ASMWD). Since the filters used in our descriptor are direction-sensitive and able to robustly reconstruct the signals with a finite number of scales, it makes our descriptor be intrinsic-symmetry unambiguous, compact as well as efficient. The extensive experimental results demonstrate that our method achieves significant performance than several state-of-the-art methods when applied in vertex-wise shape matching. © 2018 The Author(s).

关键词： Wavelet transforms

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

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arXiv 2021年

作者： Zhan, Chengjie 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 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. © 2021, CC BY-NC-ND.

关键词： Two phase flow

Projected Euler method for stochastic delay differential equation under a global monotonicity condition

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arXiv 2018年

作者： Li, Min Huang, Chengming 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

This paper investigates projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We appropriately generalized the idea of C-stability and B-consistency given by Beyn et al. [J. Sci. Comput. 67 (2016), no. 3, 955-987] to the case with delay. Moreover, the method is proved to be convergent with order 1/2 in a succinct way. Finally, some numerical examples are included to illustrate the obtained theoretical results. Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

The Nehari manifold for fractional p-Laplacian system involving concave-convex nonlinearities and sign-changing weight functions

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arXiv 2017年

作者： Zhen, Maoding 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 consider a fractional p-Laplacian system (1.1) with both concave-convex nonlinearities and sign-changing weight functions in bounded domains. With the help of the Nehari manifold, we prove that the system has at least two nontrivial solutions when the pair of the parameters (λ, µ) belongs to a certain subset of Rn . Copyright © 2017, The Authors. All rights reserved.

关键词： Laplace transforms