China Three Goeges University

Yichang, China

China Three Goeges University

Yichang, China
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Fenghong L.,Shanghai University of Electric Power | Weidong W.,China Three Goeges University
Acta Mathematica Scientia | Year: 2010

Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affine isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affine isoperimetric inequality are established for Lp-mixed curvature images. © 2010 Wuhan Institute of Physics and Mathematics.


Zhang X.,China Three Goeges University | Ouyang J.,Northwestern Polytechnical University
Yingyong Jichu yu Gongcheng Kexue Xuebao/Journal of Basic Science and Engineering | Year: 2011

The characteristic based split(CBS)method was extended into the meshfree method, namely the meshfree CBS method was proposed for the non-isotheral incompressible flow problem. First, because this method was based on the split method, it avoided the BB condition and allowed the equal order basis for the velocity and the pressure. On the other hand, because this method was also discretized by the characteristic Galerkin(CG)method, it eliminated the spurious oscillations when the convection was dominated. Moreover, this method was not involved the choice of stability parameters which was dependent on mesh. Finally, the natural convection in a square cavity was simulated and the numerical results show that the meshfree CBS method can overcome spurious oscillations of velocity and temperature when the convection is dominated; meanwhile it can also eliminate numerical instability due to the improper coupling of velocity and pressure. Additionally, it is also observed that this method has fair stability and good accuracy.


Zhang X.,China Three Goeges University | Zhang P.,China Three Goeges University
Engineering Analysis with Boundary Elements | Year: 2015

In this paper, the two-dimensional natural convection problems in complex geometries were solved by using the variational multiscale element free Galerkin (VMEFG) method. The VMEFG method is a meshless method which coupled element free Galerkin method and variational multiscale method, thus it inherits the advantages of variational multiscale and meshless methods. In this method, the field variables are decomposed into coarse and fine scales first, then solved fine scale problem analytically by using bubble functions, in the process, the stabilization parameters had appeared naturally. Moreover, it ensures that the resultant formulations yield a consistent stabilized method. From the viewpoint of application, the presented method can employ equal order basis for pressure and velocity, which is not only easy to implement but also avoid the restriction of the Babu͉ka-Brezzi condition and eliminate non-physical oscillations. Several test problems, including natural convection in the semicircular cavity, triangular cavity and triangular cavity with zig-zag shaped bottom wall are considered to investigate the accuracy of the proposed method. The numerical results obtained using VMEFG showed very good agreement with those available in the literature. © 2015 Elsevier Ltd. All rights reserved.


Zhang X.,China Three Goeges University | Zhang P.,China Three Goeges University | Zhang L.,CAS Institute of Process Engineering
Engineering Analysis with Boundary Elements | Year: 2013

In the paper an improved element free Galerkin method is presented for heat conduction problems with heat generation and spatially varying conductivity. In order to improve computational efficiency of meshless method based on Galerkin weak form, the nodal influence domain of meshless method is extended to have arbitrary polygon shape. When the dimensionless size of the nodal influence domain approaches 1, the Gauss quadrature point only contributes to those nodes in whose background cell the Gauss quadrature point is located. Thus, the bandwidth of global stiff matrix decreases obviously and the node search procedure is also avoided. Moreover, the shape functions almost possess the Kronecker delta function property, and essential boundary conditions can be implemented without any difficulties. Numerical results show that arbitrary polygon shape nodal influence domain not only has high computational accuracy, but also enhances computational efficiency of meshless method greatly. © 2013 Elsevier Ltd.


Zhang X.,China Three Goeges University | Zhang P.,China Three Goeges University
Yingyong Lixue Xuebao/Chinese Journal of Applied Mechanics | Year: 2013

In order to improve the computational efficiency of meshless methods based on Galekrin weak form for solving transient heat conduction problems, in this paper two schemes are proposed. The first one is to extend the meshless shape function to have an arbitrary convex-polygon nodal influence domain in discrete space. Then by choosing a proper factor of nodal influence radius and making the Gauss quadrature points in background cell only contribute to the meshless nodes which are located in this background cell, the node search process is avoided and the bandwidth of the stiffness matrix of the system is reduced. Meanwhile, if the factor of nodal influence radius is 1.01, the shape function almost possesses interpolation property. The second one is that when stiffness matrix is solved, mass lumping procedure is introduced to avoid the solution of the system equations, which can decrease the computational cost remarkably. Two-dimensional numerical results of rectangular region and two-dimensional circular area for transient heat conduction problems show that arbitrary polygonal nodal influence domain and mass lumping technique not only have higher calculation accuracy, but also enhance computational efficiency of meshless methods greatly. Compared with the traditional meshless method, the computing time of the arbitrary polygonal nodal influence domain is reduced 44% at least, and that of mass lumping technique is reduced 76% at least. Additionally, when the factor of nodal influence domain is 1.01, the imposition of essential boundary condition is simplified as that of the FEM. Finally, because the meshless method using mass lumping technique has lower accuracy than that using the arbitrary polygonal nodal influence domain, mass lumping technique is recommended for consideration of computational efficiency only (if the demand of accuracy is not very high, namely the error is less than 5%). On the other hand, if both the computational efficiency and the accuracy are demanded to be high, the arbitrary polygonal nodal influence domain is suggested.


Zhang X.H.,China Three Goeges University | Xiang H.,China Three Goeges University
Applied Mechanics and Materials | Year: 2014

An improved element free Galerkin method coupled the precise time-step integration method in the time domain is proposed for solving transient heat conduction problem with spatially varying conductivity in the paper. Firstly the nodal influence domain of element free Galerkin methods is extended to arbitrary convex polygon rather than rectangle and circle. When the dimensionless size of the nodal influence domain is 1.01, the shape function almost possesses interpolation property, thus essential boundary conditions can be implemented without any difficulties for the meshless method. Secondly, the precise time-step integration method is selected for the time discretization in order to improve the computational efficiency. Lastly, one numerical example is given to illustrate the highly accurate and efficient algorithm. © (2014) Trans Tech Publications, Switzerland.


Zhang X.,China Three Goeges University | Xiang H.,China Three Goeges University
Engineering Analysis with Boundary Elements | Year: 2014

This paper presents the variational multiscale element free Galerkin method to solve convection-diffusion-reaction equation. The equation under consideration involves a small diffusivity and a large reaction coefficient, which leads to reaction-convection dominated problem. The variational multiscale element free Galerkin method is derived based on Hughes's variational multiscale formulation and element free Galerkin method, thus it inherits the advantages of variational multiscale and meshless methods, meanwhile, the formulation is free of any user-defined parameters owing to the stabilization parameter arises naturally. In order to investigate the presented method, both steady and unsteady 2D convection-diffusion-reaction problems are considered, and the numerical results illustrate the proposed method has the high accuracy and stability for solving convection-diffusion-reaction equation. © 2014 Elsevier Ltd.


Zhang X.,China Three Goeges University | Xiang H.,China Three Goeges University
International Journal of Heat and Mass Transfer | Year: 2015

In order to improve computational efficiency of meshless methods based on Galerkin weak form, a fast and efficient method based on the proper orthogonal decomposition (POD) technique for transient heat conduction problems is proposed in the paper. At the first stage of the proposed method numerical simulation results or experiment data are collected as snapshots, then singular value decomposition (SVD) is applied to obtain the optimal POD basis, subsequently POD in conjunction with meshless method is used to generate the reduced model. The efficient and accuracy of the provided algorithm are examined by three examples, and the numerical examples illustrate that the meshless methods coupled with POD technique not only keeps computational accuracy, but also brings significant computational time saving for solving transient heat conduction problems. © 2015 Elsevier Ltd. All rights reserved.


Zhang X.,China Three Goeges University | Zhang P.,China Three Goeges University
Numerical Heat Transfer, Part B: Fundamentals | Year: 2014

In this article an improved element-free Galerkin method is proposed to solve heat conduction problems with heterogeneous media. Because the method almost possesses interpolation property, the implementation of essential boundary condition is as simple as that in the finite-element method. In order to validate the proposed method, several heat conduction problems with different degrees of heterogeneity are presented. In these test problems, we focus on the influence of nodal distribution to the proposed method for heat conduction problems with heterogeneous media. It is shown that, for different degrees of heterogeneity, regardless of matter whether the node is located on the interface, accurate solutions can be obtained by the proposed method for heterogeneous heat conduction problems without a source term. © 2014 Copyright Taylor & Francis Group, LLC.


Zhang X.,China Three Goeges University | Zhang P.,China Three Goeges University | Zhang L.,Dalian University
Procedia Engineering | Year: 2012

In order to improve computational efficiency of meshless methods based on Galerkin weak form, in the paper a simple technique is proposed, that is, the nodal influence domain of meshless methods is extended to arbitrary shape. Specifically, circle and rectangle nodal influence domains which are primarily used in meshless methods are generalized to arbitrary convex polygon. When the dimensionless size of the nodal influence domain approaches to 1, the Gauss quadrature point only contributes to these nodes in whose background cell the Gauss quadrature point is located. Thus, the band width of stiff matrix decreases obviously. Meanwhile, the node search process is not needed. The results obtained using the current technique have been compared with those obtained using the finite element method and meshless method with rectangle nodal influence domain, and they present that the provided technique not only has high calculation accuracy, but also enhances computational efficiency of meshless methods greatly. In addition, the technique simplifies imposition of essential boundary conditions as that of the finite element method. © 2011 Published by Elsevier Ltd.

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