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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. Source


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. Source


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. Source


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. Source


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. Source

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