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Article

Yunxia Sun, Xufeng Xiao, Zhiming Gao and Xinlong Feng

The purpose of this paper is to propose an efficient space-time operator-splitting method for the high-dimensional vector-valued Allen–Cahn (AC) equations. The key of the…

Abstract

Purpose

The purpose of this paper is to propose an efficient space-time operator-splitting method for the high-dimensional vector-valued Allen–Cahn (AC) equations. The key of the space-time operator-splitting is to devide the complex partial differential equations into simple heat equations and nolinear ordinary differential equations.

Design/methodology/approach

Each component of high-dimensional heat equations is split into a series of one-dimensional heat equations in different spatial directions. The nonlinear ordinary differential equations are solved by a stabilized semi-implicit scheme to preserve the upper bound of the solution. The algorithm greatly reduces the computational complexity and storage requirement.

Findings

The theoretical analyses of stability in terms of upper bound preservation and mass conservation are shown. The numerical results of phase separation, evolution of the total free energy and total mass conservation show the effectiveness and accuracy of the space-time operator-splitting method.

Practical implications

Extensive 2D/3D numerical tests demonstrated the efficacy and accuracy of the proposed method.

Originality/value

The space-time operator-splitting method reduces the complexity of the problem and reduces the storage space by turning the high-dimensional problem into a series of 1D problems. We give the theoretical analyses of upper bound preservation and mass conservation for the proposed method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Yuan Ping, Haiyan Su and Xinlong Feng

The purpose of this paper is to propose a local parallel finite element algorithm based on fully overlapping domain decomposition technique to solve the incompressible…

Abstract

Purpose

The purpose of this paper is to propose a local parallel finite element algorithm based on fully overlapping domain decomposition technique to solve the incompressible magnetohydrodynamic equations.

Design/methodology/approach

The algorithm uses a lower-order element pair to compute an initial approximation by the Oseen-type iteration and uses a higher-order element pair to solve a linear system in each processor.

Findings

Besides, the convergence analysis of local parallel finite element algorithm is given. Finally, numerical experiments are presented to verify the efficiency of the proposed algorithm.

Originality/value

Compared with the numerical solution of the common two-step method, this method is easy to realize and can produce a more accurate solution. And, this approach is executed in parallel, so it saves a lot of computational time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Yuan Ping, Haiyan Su, Jianping Zhao and Xinlong Feng

This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural…

Abstract

Purpose

This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural convection problem.

Design/methodology/approach

The first-order implicit Euler formula and second-order Crank–Nicolson formula are used to time discretization respectively. Each processor of the algorithms computes a stabilized solution in its own global composite mesh in parallel. These algorithms compute a nonlinear system for the velocity, pressure and temperature based on a lower-order element pair (P1b-P1-P1) and solve a linear approximation based on a higher-order element pair (P2-P1-P2) on the same mesh, which shows that the new algorithms have the same convergence rate as the two-step finite element methods. What is more, the stability analysis of the proposed algorithms is derived. Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms.

Findings

Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms.

Originality/value

The novel parallel two-step algorithms for incompressible natural convection problem are proposed. The rigorous analysis of the stability is given for the proposed parallel two-step algorithms. Extensive 2D/3D numerical tests demonstrate that the parallel two-step algorithms can deal with the incompressible natural convection problem for high Rayleigh number well.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Gang Peng, Zhiming Gao, Wenjing Yan and Xinlong Feng

This paper aims to consider numerical simulation for radionuclide transport calculations in geological radioactive waste repository.

Abstract

Purpose

This paper aims to consider numerical simulation for radionuclide transport calculations in geological radioactive waste repository.

Design/methodology/approach

The nonlinear two-point flux approximation is used to discretize the diffusion flux and has a fixed stencil. The cell-vertex unknowns are applied to define the auxiliary unknowns and can be interpolated by the cell-centered unknowns. The approximation of convection flux is based on the second-order upwind method with a slope limiter.

Findings

Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes.

Originality/value

A new positivity-preserving nonlinear finite volume scheme is proposed to simulate the far-field model used in the geological radioactive waste repository. Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Weilong Wang, Jilian Wu and Xinlong Feng

The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to…

Abstract

Purpose

The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem.

Design/methodology/approach

The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P2, P2, P1, P2) to approximate the density, velocity, pressure and temperature field.

Findings

The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

Originality/value

Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Lulu Li, Haiyan Su, Jianping Zhao and Xinlong Feng

This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method.

Abstract

Purpose

This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method.

Design/methodology/approach

The optimal error estimates of the penalty FEM are established by using the lower-order finite element pair P1-P0-P1 which does not satisfy the discrete inf-sup condition. Besides, a new recovery type posteriori estimator in view of the gradient recovery and superconvergent theory to deal with the discontinuity of the gradient of numerical solution.

Findings

The stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.

Originality/value

The provided reliability and efficiency analysis is shown that the true error can be effectively bounded by the recovery-based error estimator.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Xufeng Xiao, Dongwei Gui and Xinlong Feng

This study aims to present a highly efficient operator-splitting finite element method for the nonlinear two-dimensional/three-dimensional (2D/3D) Allen–Cahn (AC) equation…

Abstract

Purpose

This study aims to present a highly efficient operator-splitting finite element method for the nonlinear two-dimensional/three-dimensional (2D/3D) Allen–Cahn (AC) equation which describes the anti-phase domain coarsening in a binary alloy. This method is presented to overcome the higher storage requirements, computational complexity and the nonlinear term in numerical computation for the 2D/3D AC equation.

Design/methodology/approach

In each time interval, the authors first split the original equation into a heat equation and a nonlinear equation. Then, they split the high-dimensional heat equation into a series of one-dimensional (1D) heat equations. By solving each 1D subproblem, the authors obtain a numerical solution for heat equation and take it as an initial for the nonlinear equation, which is solved analytically.

Findings

The authors show that the proposed method is unconditionally stable. Finally, various numerical experiments are presented to confirm the high accuracy and efficiency of this method.

Originality/value

A new operator-splitting method is presented for solving the 2D/3D parabolic equation. The 2D/3D parabolic equation is split into a sequence of 1D parabolic equations. In comparison with standard finite element method, the present method can save much central processing unit time. Stability analysis and error estimates are derived and numerical results are presented to support the theoretical analysis.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Qiaolei Sun, Liang He, Ding Feng, Xinlong Chen, Liangliang Ding and Yiliu Tu

As the excessive lifting force can lead to catwalk rollover and well site accidents, the lifting process boundary conditions and structural parameters have a significant…

Abstract

Purpose

As the excessive lifting force can lead to catwalk rollover and well site accidents, the lifting process boundary conditions and structural parameters have a significant effect lifting force, it is important to analysis the structural parameters on the maximum lifting force in the lifting process of power catwalk.

Design/methodology/approach

A new model is proposed to analyze the influence of structure parameters on its lifting force for lifting power catwalk in this paper, and the geometric and dynamic equations are established according to the different boundary conditions in different stages. In addition, the establishment of dynamics equations is based on D'Alembert's principle. To solve the model, dynamic analysis software is developed, which uses c # call MATLAB to solve the geometric and dynamic equations. The maximum lifting force is analyzed and optimized according to the software, the influence of structural parameters on the maximum lifting force is obtained and the correctness of the optimization is proved by experiments.

Findings

The best value of offset e is 0. The length of L22 should as small as possible while the installation size of the end of the conveying arm are guaranteed. The length of L1 should as small as possible while ensuring the not exceed the maximum value. The maximum lifting force remain the same in the second phase, the maximum lifting force decreases with the increase of Lcp, Lcpshould as small as possible. The maximum pressure of the hydraulic oil dropped by an average of 13.62% under optimized parameters.

Practical implications

This paper provides a theoretical basis for the selection of hydraulic winch, which also provides the theoretical basis and data support for the design and optimization of the structural parameters of the power catwalk.

Social implications

This research has industrial applications in SJ Petroleum Machinery CO.LTD, SINOPEC (China) .CANRIG, North Rig, TESCO, Sichuan HONGHUA petroleum equipment CO.LTD of CNPC., Baoji Oil field Machinery CO.LTD, SJ Petroleum Machinery Co. LTD of SINOPEC, Yantai Jereh Oilfield Services Group CO.LTD, Nanyang clips oil equipment (group) CO. LTD, etc are the likely users.

Originality/value

A new model is proposed to analyze the lifting force of lifting power catwalk. The model takes into account the inertia force of the structure, development of dynamics software and analysis and optimization of structural parameters. The maximum lifting force is analyzed and optimized according to the software, the influence of structural parameters on the maximum lifting force is obtained and the correctness of the optimization is proved by experiments.

Details

Journal of Engineering, Design and Technology , vol. 19 no. 1
Type: Research Article
ISSN: 1726-0531

Keywords

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