检索结果-内蒙古大学图书馆

Convergence analysis of Hermite approximations for analytic functions

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Wang, Haiyong Zhang, Lun 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 School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics Fudan University Shanghai200433 China

In this paper, we present a rigorous analysis of root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are analytic in an infinite strip containing the real axis and satisfy certain restrictions on the asymptotic behavior at infinity within this strip. Asymptotically sharp error bounds in the weighted and maximum norms are derived. The key ingredients of our analysis are some remarkable contour integral representations for the Hermite coefficients and the remainder of Hermite spectral interpolations. Further extensions to Gauss-Hermite quadrature, Hermite spectral differentiations, generalized Hermite spectral approximations and the scaling factor of Hermite approximation are also discussed. Numerical experiments confirm our theoretical *** Codes 41A25, 41A10 Copyright © 2023, The Authors. All rights reserved.

关键词： Interpolation

Lattice boltzmann modeling of wall-bounded ternary fluid flows

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Liang, Hong Xu, Jiangrong Chen, Jiangxing Chai, Zhenhua Shi, Baochang Department of Physics Hangzhou Dianzi University Hangzhou310018 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

In this paper, a wetting boundary scheme used to describe the interactions among ternary fluids and solid is proposed in the framework of the lattice Boltzmann method. This scheme for three-phase fluids can preserve the reduction consistency property with the diphasic situation such that it could give physically relevant results. Combining this wetting boundary scheme and the lattice Boltzmann (LB) ternary fluid model based on the multicomponent phase-field theory, we simulated several ternary fluid flow problems involving solid substrate, including the spreading of binary drops on the substrate, the spreading of a compound drop on the substrate, and the shear of a compound liquid drop on the substrate. The numerical results are found to be good agreement with the analytical solutions or some available results. Finally, as an application, we use the LB model coupled with the present wetting boundary scheme to numerically investigate the impact of a compound drop on a solid circular cylinder. It is found that the dynamics of a compound drop can be remarkably influenced by the wettability of the solid surface and the dimensionless Weber number. Copyright © 2017, The Authors. All rights reserved.

关键词： Circular cylinders

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Liang, Hong Xu, Jiangrong Chen, Jiangxing Wang, Huili Chai, Zhenhua Shi, Baochang Department of Physics Hangzhou Dianzi University Hangzhou310018 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

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and Spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. At last, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature. Copyright © 2017, The Authors. All rights reserved.

关键词： Navier Stokes equations

Analysis of multivariate Gegenbauer approximation in the hypercube

学校读者我要写书评

暂无评论

arXiv 2018年

In this paper, we are concerned with multivariate Gegenbauer approximation of analytic functions defined in the d-dimensional hypercube. Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion are presented based on two different extensions of the Bernstein ellipse. We then establish an explicit error bound for the multivariate Gegenbauer approximation associated with an q ball index set in the uniform norm. As an application, we extend our arguments to obtain some new tight bounds for the coefficients of tensorized Legendre expansions in the context of polynomial approximation of parameterized *** Codes 41A10, 41A63, 41A25 Copyright © 2018, The Authors. All rights reserved.

关键词： Geometry

A generalized lattice boltzmann model for fluid flow system and its application in two-phase flows

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Yuan, Xiaolei Chai, Zhenhua Wang, Huili 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 School of Mathematics and Computer Science Wuhan Textile University Wuhan430073

In this paper, a generalized lattice Boltzmann (LB) model with a mass source is proposed to solve both incompressible and nearly incompressible Navier-Stokes (N-S) equations. This model can be used to deal with single-phase and twophase ows problems with a mass source term. From this generalized model, we can not only get some existing models, but also derive new models. Moreover, for the incompressible model derived, a modified pressure scheme is introduced to calculate the pressure, and then to ensure the accuracy of the model. In this work, we will focus on a two-phase ow system, and in the frame work of our generalized LB model, a new phase-field-based LB model is developed for incompressible and quasi-incompressible two-phase ows. A series of numerical simulations of some classic physical problems, including a spinodal decomposition, a static droplet, a layered Poiseuille ow, and a bubble rising ow under buoyancy, are performed to validate the developed model. Besides, some comparisons with previous quasi-incompressible and incompressible LB models are also carried out, and the results show that the present model is accurate in the study of two-phase ows. Finally, we also conduct a comparison between quasiincompressible and incompressible LB models for two-phase ow problems, and find that in some cases, the proposed quasi-incompressible LB model performs better than incompressible LB models. Copyright © 2019, The Authors. All rights reserved.

关键词： Two phase flow

Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Wang, Nan Li, Meng Huang, Chengming School of Mathematics and Statistics Zhengzhou University Zhengzhou450001 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

In this paper, we consider a second-order scalar auxiliary variable (SAV) Fourier spectral method to solve the nonlinear fractional generalized wave equation. Unconditional energy conservation or dissipation properties of the fully discrete scheme are first established. Next, we utilize the temporal-spatial error splitting argument to obtain unconditional optimal error estimate of the fully discrete scheme, which overcomes time-step restrictions caused by strongly nonlinear system, or the restrictions that the nonlinear term needs to satisfy the assumption of global Lipschitz condition in all previous works for fractional undamped or damped wave equations. Finally, some numerical experiments are presented to confirm our theoretical analysis. Copyright © 2021, The Authors. All rights reserved.

关键词： Energy dissipation

The influence of stochastic forcing on strong solutions to the Incompressible Slice Model in 2D bounded domain

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Zhang, Lei Shi, Yu Hu, Chaozhu Wang, Weifeng Liu, Bin 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 SCIENCE WUHAN UNIVERSITY OF TECHNOLOGY HUBEI WUHAN 430070 China SCHOOL OF SCIENCE HUBEI UNIVERSITY OF TECHNOLOGY HUBEI WUHAN 430068 China SCHOOL OF MATHEMATICS AND STATISTICS SOUTH-CENTRAL UNIVERSITY FOR NATIONALITIES WUHAN430074 China

The Cotter-Holm Slice Model (CHSM) was introduced to study the behavior of whether and specifically the formulation of atmospheric fronts, whose prediction is fundamental in meteorology. Considered herein is the influence of stochastic forcing on the Incompressible Slice Model (ISM) in a smooth 2D bounded domain, which can be derived by adapting the Lagrangian function in Hamilton’s principle for CHSM to the Euler-Boussinesq Eady incompressible case. First, we establish the existence and uniqueness of local pathwise solution (probability strong solution) to the ISM perturbed by nonlinear multiplicative stochastic forcing in Banach spaces Wk, p(D) with k > 1 + 1/ p and p ≥ 2. The solution is obtained by introducing suitable cut-off operators applied to the W1,∞-norm of the velocity and temperature fields, using the stochastic compactness method and the Yamada-Watanabe type argument based on the Gyöngy-Krylov characterization of convergence in probability. Then, when the ISM is perturbed by linear multiplicative stochastic forcing and the potential temperature does not vary linearly on the y-direction, we prove that the associated Cauchy problem admits a unique global-in-time pathwise solution with high probability, provided that the initial data is sufficiently small or the diffusion parameter is large enough. The results partially answer the problems left open in Alonso-Orán et al. (Physica D 392:99–118, 2019, pp. 117). Copyright © 2020, The Authors. All rights reserved.

关键词： Banach spaces

Phase-field-based lattice boltzmann model for immiscible incompressible n-phase flows

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Yuan, Xiaolei Liang, Hong 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 Department of Physics Hangzhou Dianzi University Hangzhou310018 China

In this paper, we develop an efficient lattice Boltzmann (LB) model for simulating immiscible incompressible N-phase ows (N ≥ 2) based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the N-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, (N -1) LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible N-phase uid ows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four uid phases and dynamics of droplets and interfaces for five uid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among N (N ≥ 2) immiscible incompressible ows. Copyright © 2019, The Authors. All rights reserved.

关键词： Navier Stokes equations

Markus–Yamabe Conjecture for Asymptotic Stability of Planar Piecewise Linear Systems

学校读者我要写书评

暂无评论

Research Square

Research Square 2021年

作者： Zhang, Yuhong Yang, Xiao-Song School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Science Computing Huazhong University of Science and Technology Wuhan430074 China

We present in this paper a detailed study on the Markus–Yamabe conjecture in planar piecewise linear systems. We consider discontinuous piecewise linear systems with two zones separated by a straight line, in which every subsystem is asymptotically stable. We prove the existence of limit cycles under explicit parameter conditions and give more different counterexamples to the Markus-Yamabe conjecture in addition to the counterexamples given by Llibre and Menezes. In particular, we consider continuous planar piecewise linear systems. For such a system with n + 1 zones separated by n parallel straight lines in phase space, we prove that if each of subsystems is asymptotically stable, then this system has a globally asymptotically stable equilibrium point, therefore the Markus–Yamabe conjecture still holds. Some examples are given to illustrate the main results. © 2021, CC BY.

关键词： Asymptotic stability