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Numerical analysis of density flows in adiabatic two-phase fluids through characteristic finite element method

INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 2019年第1-2期33卷 23-33页

作者： Kawahara, Mutsuto Fukuyama, Kohei Chuo Univ Dept Civil Engn Tokyo Japan

The purpose of this study is to analyze the density flow in adiabatic two-phase fluids through the characteristic finite element method. The fluids are assumed to be liquids. The equations of conservations of mass and momentum for the adiabatic flows and the Birch-Murnaghan equation of state are employed as the governing equations. The employed finite element method is a combination of the characteristic method and the implicit method. The governing equations are divided into two parts: the advection part and the non-advection part. The characteristic method is applied to the advection part. The Hermite interpolation function, which is based on the complete third-order polynomial interpolation using triangular finite element is employed for the interpolation of both velocity and density. Using the discontinuity conditions, an interface translocation method can be derived. The interface of the two flow densities are interpolated through the third-order spline function, using which the curvature of the interface can be directly computed. For the numerical study, the development of density flow over the Tokyo bay is presented. It is detected out that high density area is abruptly diffused over the whole area. According to the differences in the two densities, various flow patterns are computed.

关键词： characteristic finite element method two-phase flow Birch-Murnaghan equation of state Hermite interpolation function interface condition Tokyo bay

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A characteristic finite element method FOR CONSTRAINED CONVECTION-DIFFUSION-REACTION OPTIMAL CONTROL PROBLEMS

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Journal of Computational Mathematics 2013年第1期31卷 88-106页

作者： Hongfei Fu Hongxing Rui Hui Guo Department of Computational and Applied Mathematics China University of Petroleum Qingdao 266580 China School of Mathematics Shandong University Jinan 250100 China

In this paper, we develop a priori error estimates for the solution of constrained convection-diffusion-reaction optimal control problems using a characteristic finite element method. The cost functional of the optimal control problems consists of three parts： The first part is about integration of the state over the whole time interval, the second part refers to final-time state, and the third part is a regularization term about the control. We discretize the state and co-state by piecewise linear continuous functions, while the control is approximated by piecewise constant functions. Pointwise inequality function constraints on the control are considered, and optimal a L2-norm priori error estimates are obtained. Finally, we give two numerical examples to validate the theoretical analysis.

关键词： characteristic finite element method Constrained optimal control Convection-diffusion-reaction equations Pointwise inequality constraints A priori error estimates.

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A characteristic finite element method for optimal control problems governed by convection-diffusion equations

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第3期235卷 825-836页

作者： Fu, Hongfei China Univ Petr Sch Math & Computat Sci Dongying 257061 Peoples R China

In this paper we analyze a characteristic finite element approximation of convex optimal control problems governed by linear convection-dominated diffusion equations with pointwise inequality constraints on the control variable, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by either piecewise constant functions or piecewise linear discontinuous functions. A priori error estimates are derived for the state, co-state and the control. Numerical examples are given to show the efficiency of the characteristic finite element method. (C) 2010 Elsevier B.V. All rights reserved.

关键词： characteristic finite element method Optimal control problems Convection-diffusion equations Pointwise inequality constraints A priori error estimates

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Two-grid method for miscible displacement problem by mixed finite element methods and finite element method of characteristics

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第11期72卷 2694-2715页

作者： Hu, Hanzhang Chen, Yanping Zhou, Jie South China Normal Univ Sch Math Sci Guangzhou 520631 Guangdong Peoples R China Jiaying Univ Sch Math Meizhou 514015 Peoples R China Xiangtan Univ Sch Math & Computat Sci Xiangtan 411105 Hunan Peoples R China

The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations. One is elliptic form equation for the pressure and the other is parabolic form equation for the concentration of one of the fluids. Since only the velocity and not the pressure appears explicitly in the concentration equation, we use a mixed finite element method for the approximation of the pressure equation and finite element method with characteristics for the concentration equation. To linearize this full discrete scheme problems, we use two Newton iterations on the fine grid in our methods, with the initial guess coming from the coarse-grid solution. Then, we get the error estimates for the three-step two-grid algorithms. It is showed that coarse space can be extremely coarse and we achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = .O(h(1/4)) in the three-step algorithm. Finally, numerical experiment indicates that two-grid algorithm is very effective. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Two-grid method Miscible displacement problem Mixed finite element method characteristic finite element method

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Two-grid method for miscible displacement problem with dispersion by finite element method of characteristics

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ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 2021年第3期101卷

作者： Chen, Yanping Hu, Hanzhang South China Normal Univ Sch Math Sci Guangzhou 510631 Guangdong Peoples R China Jiaying Univ Sch Math Meizhou 514015 Guangdong Peoples R China

A combined method consisting of the mixed finite element method for the pressure equation and finite element method with characteristics for the concentration equation is proposed to solve the coupled system of incompressible two-phase flow in porous media. Two-grid algorithm based on the Newton iteration method is developed and analyzed for the nonlinear coupled system. It is shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy as long as the mesh sizes satisfyH=O(h1/2).

关键词： characteristic finite element method miscible displacement problem mixed finite element two-grid method

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Discrepancy between theory and real computation on the stability of some finite element schemes

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2007年第2期199卷 424-431页

作者： Tabata, Masahisa Kyushu Univ Fac Math Fukuoka 8128581 Japan

finite element schemes based on the method of characteristics are considered for the convection-diffusion equation. Those are proved to be stable, but in a real computation some instability occurs. We reveal the cause of the discrepancy between theory and real computation, and present a remedy to the instability. (c) 2006 Elsevier B.V. All rights reserved.

关键词： stability characteristic finite element method numerical integration error convection-diffusion equation

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An evaluation model for the effect of adsorption boundary on pollutant degradation in water areas

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WATER SUPPLY 2019年第3期19卷 771-777页

作者： Liu, Haitao Liu, Zhiping Sun, Shuangke Li, Guangning Zheng, Tiegang China Inst Water Resources & Hydropower Res State Key Lab Simulat & Regulat Water Cycle River Beijing 100038 Peoples R China

A two-dimensional water quality numerical model has been developed to analyse the influence of adsorption boundary on the variation of water pollutant degradation. The characteristic finite element method is adopted to solve the discrete pollutant concentration equations, so the time-monotonicity of concentration is ensured in the convection-dominated flow field with various adsorption conditions. The second-order Runge-Kutta method is adopted to track the upstream concentration source points along the streamline, so the precision of the calculated pollutant concentration is improved even under the streamline sharp-bending condition. The flow roughness and pollutant degradation coefficient are formulated by elements according to the actual situation, so the model can quantitatively analyse the effect of various ecological restoration schemes on purification capacity in water areas. The adaptability and robustness of the model were verified by a typical engineering case, where the calculated results coincide with the measured data.

关键词： adsorption boundary characteristic finite element method ecological restoration evaluation pollutant degradation

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A characteristic finite element two-grid algorithm for a compressible miscible displacement problem

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2020年第2期46卷 15-15页

作者： Hu, Hanzhang Chen, Yanping Huang, Yunqing Jiaying Univ Sch Math Meizhou 514015 Guangdong Peoples R China South China Normal Univ Sch Math Sci Guangzhou 510631 Guangdong Peoples R China Xiangtan Univ Hunan Key Lab Computat & Simulat Sci & Engn Sch Math & Computat Sci Xiangtan 411105 Hunan Peoples R China

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. A mixed finite element method is employed to approximate the pressure and the Darcy velocity, and a characteristic finite element method is used to approximate the concentration. Twice Newton iteration is applied on the fine grid to linearize the fully discrete problem using the coarse-grid solution as the initial guess. Moreover, the L-q error estimates are conducted for the pressure, Darcy velocity, and concentration variables in the two-grid solutions. It is shown both theoretically and numerically that the coarse space can be extremely coarse, with no loss in the order of accuracy, and the two-grid algorithm still achieves the optimal approximation as long as the mesh sizes satisfy H=O(h(1/4)). The numerical results show that this algorithm is very effective.

关键词： Two-grid method Compressible miscible displacement problem Mixed finite element method characteristic finite element method

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