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A FINITE ELEMENT ALGORITHM FOR NEMATIC LIQUID CRYSTAL FLOW BASED ON THE GAUGE-UZAWA METHOD

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Journal of Computational Mathematics 2022年第1期40卷 26-43页

作者： pengzhan huang Yinnian He Ting Li College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

In this paper,we present a finite element algorithm for the time-dependent nematic liquid crystal flow based on the Gauge-Uzawa *** algorithm combines the Gauge and Uzawa methods within a finite element variational formulation,which is a fully discrete projection type algorithm,whereas many projection methods have been studied without space ***,error estimates for velocity and molecular orientation of the nematic liquid crystal flow are ***,numerical results are given to show that the presented algorithm is reliable and confirm the theoretical analysis.

关键词： Nematic liquid crystal model Finite element approximation Gauge-Uzawa method Error analysis

SECOND ORDER UNCONDITIONALLY STABLE AND CONVERGENT LINEARIZED SCHEME FOR A FLUID-FLUID INTERACTION MODEL

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Journal of Computational Mathematics 2023年第1期41卷 72-93页

作者： Wei Li pengzhan huang Yinnian He College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830017China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

In this paper,a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model,which consists of two Navier-Stokes equations coupled by a linear interface *** proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization,the secondorder backward differentiation formula for temporal discretization,the second-order Gear’s extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear ***,the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also ***,some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

关键词： Fluid-fluid interaction model Unconditional stability Second order temporal accuracy Error estimate

Convergence and stability of two-level penalty mixed finite element method for stationary Navier-Stokes equations

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Frontiers of Mathematics in China 2013年第4期8卷 837-854页

作者： pengzhan huang Yinnian HE Xinlong FENG College of Mathematics and System Sciences Xinjiang University Urumqi 830046 China School of Mathematics and Statistics Xi'an Jiaotong University Xi'an 710049 China

The two-level penalty mixed finite element method for the stationary Navier-Stokes equations based on Taylor-Hood element is considered in this paper. Two algorithms are proposed and analyzed. Moreover, the optimal stability analysis and error estimate for these two algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms.

关键词： Navier-Stokes equation level strategy Taylor-Hood element penalty mixed finite element method two-error estimate stability analysis

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

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Acta Mathematica Scientia 2021年第2期41卷 381-396页

作者： Juan WEN pengzhan huang Ya-Ling HE Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education School of Energy and Power EngineeringXi'an Jiaotong UniversityXi'an 710049China School of Sciences Xi'an University of TechnologyXi'an 710048China College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China

In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue *** new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem *** convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also ***,we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue ***,we have proved a priori error estimates for this new two-level stabilized ***,numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.

关键词： Two-level multiscale finite element method P_(1)/P_(1)elements the Stokes eigenvalue problem

向列相液晶流的模块grad-div稳定化有限元方法

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数学物理学报（A辑） 2021年第2期41卷 451-467页

作者：李婷黄鹏展新疆大学数学与系统科学学院乌鲁木齐830046

该文针对向列相液晶流,提出了一种模块grad-div稳定化有限元方法,主要是在向后欧拉格式中增加了一个后处理步骤.该方法可以惩罚原有格式的质量不守恒性,但不会随着稳定化参数的变大而使计算时间增加.此外,该文给出了向列相液晶流的速度... 详细信息

该文针对向列相液晶流,提出了一种模块grad-div稳定化有限元方法,主要是在向后欧拉格式中增加了一个后处理步骤.该方法可以惩罚原有格式的质量不守恒性,但不会随着稳定化参数的变大而使计算时间增加.此外,该文给出了向列相液晶流的速度和分子方向的误差估计,还通过数值实验验证了理论分析.

关键词：向列相液晶模型模块grad-div稳定化方法误差分析有限元方法向后欧拉方法

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流体相互作用模型的粘性分离有限元方法

数学物理学报（A辑） 2020年第5期40卷 1362-1380页

作者：李伟黄鹏展新疆大学数学与系统科学学院乌鲁木齐830046

针对流体-流体相互作用模型,研究了一种全离散的粘性分离有限元方法.该方法在时间层采用了粘性分解技术和空间混合有限元方法,其中时间项包括两个步骤.第一步,采用向后Euler方法用于时间离散化,采用半隐式方法处理非线性项,并使用几何... 详细信息

针对流体-流体相互作用模型,研究了一种全离散的粘性分离有限元方法.该方法在时间层采用了粘性分解技术和空间混合有限元方法,其中时间项包括两个步骤.第一步,采用向后Euler方法用于时间离散化,采用半隐式方法处理非线性项,并使用几何平均方法处理流体界面.然后,在第二步中,我们只解决了一个线性Stokes问题,而没有对每个单独的区域进行时间步的空间迭代.因此,粘性分离有限元方法将非线性和不可压缩性分开.此外,通过严格的分析验证了该方法的稳定性和收敛性.最后,数值实验表明了该方法的性能.

关键词：流体相互作用模型粘性分离法稳定性收敛性有限元法

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有限元实验课程教学探索

大理学院学报（综合版） 2013年第10期12卷 77-80页

作者：黄鹏展新疆大学数学与系统科学学院乌鲁木齐830046

有限元方法是一种求解偏微分方程主要的数值方法,有着许多重要的思想和技巧。学生初学时会面临许多的困难,尤其是做上机实验,即本课程——有限元实验课程的学习。那么,怎样才能让学生尽快地适应本课程的学习?如何引导学生在计算机上实... 详细信息

有限元方法是一种求解偏微分方程主要的数值方法,有着许多重要的思想和技巧。学生初学时会面临许多的困难,尤其是做上机实验,即本课程——有限元实验课程的学习。那么,怎样才能让学生尽快地适应本课程的学习?如何引导学生在计算机上实现用有限元求解偏微分方程?结合笔者的教学实践,对有限元实验课程教学进行了探索。

关键词：有限元数值模拟 Matlab FreeFem++ 偏微分方程

Navier-Stokes方程几种稳定化有限元算法数值比较

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数学物理学报（A辑） 2016年第3期36卷 543-557页

作者：文娟何银年黄鹏展李敏西安理工大学理学院西安710048 西安交通大学数学与统计学院西安710049 新疆大学数学与系统科学学院乌鲁木齐830046 云南开放大学光电工程学院昆明650223

该文比较了基于低次等阶有限元对求解定常Navier-Stokes方程的几种稳定化有限元算法.通过比较可以看出,在求解大雷诺数Navier-Stokes方程时,多尺度增量有限元算法从稳定性和计算精度方面来说是一种不错的方法.

关键词：稳定化方法 P_1/P_1有限元对 Inf-Sup条件混合有限元 Navier-Stokes方程

A thermodynamic perspective on electrode poisoning in solid oxide fuel cells

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International Journal of Minerals,Metallurgy and Materials 2024年第6期31卷 1449-1455页

作者： Kevin huang Department of Mechanical Engineering University of South CarolinaColumbiaUSA

A critical challenge to the commercialization of clean and high-efficiency solid oxide fuel cell(SOFC)technology is the insuf-ficient stack lifespan caused by a variety of degradation mechanisms,which are associated with cell components and chemical *** components related degradation refers to thermal/chemical/electrochemical deterioration of cell materials under operating conditions,whereas the latter regards impurities in feedstocks of oxidant(air)and reductant(fuel).This article provides a thermodynamic perspective on the understanding of the impurities-induced degradation mechanisms in *** discussion focuses on using thermodynamic ana-lysis to elucidate poisoning mechanisms in cathodes by impurity species such as Cr,CO_(2),H_(2)O,and SO_(2) and in the anode by species such as S(or H_(2)S),SiO_(2),and P_(2)(or PH_(3)).The author hopes the presented fundamental insights can provide a theoretical foundation for search-ing for better technical solutions to address the critical degradation challenges.

关键词： impurities air fuel reaction activity