检索结果-内蒙古大学图书馆

High-order finite volume methods for solving compressible multicomponent flows

Science China Mathematics 2025年第3期68卷 729-760页

作者： Feng Zheng Jianxian Qiu School of Mathematics and Statistics Fujian Key Laboratory of Mathematical Analysis and ApplicationFujian Normal UniversityFuzhou 350117China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, we propose a high-order finite volume method for solving multicomponent fluid problems. Our method couples the quasi-conservative form with the reconstruction of conservative variables in a characteristic manner. The source term and numerical fluxes are carefully designed to maintain the pressure and velocity equilibrium for the interface-only problem and preserve the equilibrium of physical parameters in a single-component fluid. These ingredients enable our scheme to achieve both high-order accuracy in the smooth region and the high resolution in the discontinuity region of the solution. Extensive numerical tests are performed to verify the high resolution and accuracy of the scheme.

关键词： finite volume high-order multicomponent flows

来源：评论

学校读者我要写书评

暂无评论

Cherenkov Radiation:A Stochastic Differential Model Driven by Brownian Motions

引用

Computer modeling in Engineering & Sciences 2023年第4期135卷 155-168页

作者： Qingqing Li Zhiwen Duan Dandan Yang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

With the development of molecular imaging,Cherenkov optical imaging technology has been widely *** studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion *** this paper,time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic *** on the original steady-state diffusion equation,we first propose a stochastic partial differential *** numerical solution to the stochastic partial differential model is carried out by using the finite element *** the time resolution is high enough,the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation,which may provide a new way to alleviate the problem of Cherenkov luminescent imaging *** addition,the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide inmuscle tissue are also first proposed by GEANT4Monte *** result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations,which shows that the stochastic partial differential equation can simulate the corresponding process.

关键词： Cherenkov radiation stochastic partial differential equations numerical approximation and analysis GEANT4 Monte Carlo simulation

来源：评论

学校读者我要写书评

暂无评论

ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS

引用

Acta Mathematica Scientia 2023年第4期43卷 1865-1880页

作者：韩豪张诚坚 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

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous ***,for the analytical solutions of the equations,we derive their expressions and asymptotical stability ***,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically ***,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

关键词： neutral reaction-diffusion equations piecewise continuous arguments asymptotical stability finite element methods numerical experiment

来源：评论

学校读者我要写书评

暂无评论

Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schr¨odinger Equations

引用

Numerical Mathematics(Theory,Methods and Applications) 2023年第2期16卷 348-369页

作者： Wanqiu Yuan Dongfang Li Chengjian Zhang 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

A linearized transformed L1 Galerkin finite element method(FEM)is presented for numerically solving the multi-dimensional time fractional Schr¨odinger *** optimal error estimates of the fully-discrete scheme are *** error estimates are obtained by combining a new discrete fractional Gr¨onwall inequality,the corresponding Sobolev embedding theorems and some inverse *** the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting *** examples are presented to confirm the theoretical results.

关键词： Optimal error estimates time fractional Schr¨odinger equations transformed L1 scheme discrete fractional Gr¨onwall inequality

来源：评论

学校读者我要写书评

暂无评论

ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

引用

Journal of Computational Mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun 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 Department of Mathematics University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed *** 1D problems,we construct a kind of oneparameter finite difference(OPFD)*** is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and *** implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD *** 2D problems,we develop another kind of OPFD *** such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG *** particular,we prove that ADI scheme can arrive at second-order accuracy in time and *** some numerical experiments,the computational effectiveness and accuracy of the methods are further ***,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method

来源：评论

学校读者我要写书评

暂无评论

An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

引用

Science China Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao Jianxian Qiu School of Mathematical Sciences and Institute of Natural Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

来源：评论

学校读者我要写书评

暂无评论

A DECOUPLED,LINEARLY IMPLICIT AND UNCONDITIONALLY ENERGY STABLE SCHEME FOR THE COUPLED CAHN-HILLIARD SYSTEMS

引用

Journal of Computational Mathematics 2025年第3期43卷 708-730页

作者： Dan Zhao Dongfang Li Yanbin Tang Jinming Wen 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 College of Information Science and Technology Jinan UniversityGuangzhou 510632China

We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary variable(SAV)*** only needs to solve three linear equations at each time step,where each unknown variable can be solved *** is shown that the semi-discrete scheme has second-order accuracy in the temporal *** convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different *** examples are presented to further confirm the validity of the methods.

关键词： Coupled Cahn-Hilliard system Leap-frog method Scalar auxiliary variable Error estimate

来源：评论

学校读者我要写书评

暂无评论

SHARP POINTWISE-IN-TIME ERROR ESTIMATE OF L1 SCHEME FOR NONLINEAR SUBDIFFUSION EQUATIONS

引用

Journal of Computational Mathematics 2024年第3期42卷 662-678页

作者： Dongfang Li Hongyu Qin Jiwei Zhang 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 School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

An essential feature of the subdiffusion equations with theα-order time fractional derivative is the weak singularity at the initial *** weak regularity of the solution is usually characterized by a regularity parameterσ∈(0,1)∪(1,2).Under this general regularity assumption,we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results,i.e.,a refined discrete fractional-type Grönwall inequality(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion *** present results fill the gap on some interesting convergence results of L1 scheme onσ∈(0,α)∪(α,1)∪(1,2].Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.

关键词： Sharp pointwise-in-time error estimate Ll scheme Nonlinear subdiffusion equations Non-smooth solutions

来源：评论

学校读者我要写书评

暂无评论

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

引用

Communications on Applied Mathematics and Computation 2024年第1期6卷 605-624页

作者： Feng Zheng Jianxian Qiu College of Mathematics and Statistics Fujian Normal UniversityFuzhou350117FujianChina School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High-Performance Scientific Computing Xiamen UniversityXiamen361005FujianChina

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation *** can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary ***,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO *** numerical tests are performed to verify the high resolution and high accuracy of the scheme.

关键词： Finite volume Dimension by dimension HWENO Hyperbolic conservation laws

来源：评论

学校读者我要写书评

暂无评论

A Numerical Study of the Poisson Equation with Arbitrary Domains Based on the Extrapolation Technique

A Numerical Study of the Poisson Equation with Arbitrary Dom...

引用

2022 International Conference on Mechanics and Applied Mathematics, MAM 2022

作者： Zhang, Hui Yu, Pan Shi, Xueying Li, Lin School of Mathematics and Physics and Hunan Key Laboratory for Mathematical Modeling and Scientific Computing University of South China Hengyang421001 China

The Poisson equation with arbitrary domains is considered in this paper using an extrapolation technique. The two-dimensional problem is primarily examined, and the extrapolation formulas O2 and O4 are thoroughly deduced. Not only the effect of different extrapolations on boundary point errors is analyzed, but a strategy for selecting extrapolation points is also provided. Finally, numerical accuracy results are presented. © Published under licence by IOP Publishing Ltd.

关键词： Extrapolation

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：