Variational multiscale element free Galerkin method for the water wave problems

Zhang, Lin; Ouyang, Jie; Jiang, Tao; Ruan, Chunlei

doi:10.1016/j.jcp.2011.03.026

Cited by 26 publications

(24 citation statements)

References 21 publications

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“…Until now, the implementation of essential boundary conditions is still an open research topic for meshless methods. In the paper, a simple technique proposed by Zhang et al [11,12] is utilized, which makes MLS approximation function possess interpolation property as  approach to 1 and is easier to solve problems with complex area.…”

Section: Review Of the Element Free Galerkin Methodsmentioning

confidence: 99%

“…In the third step, substitutes the fine scale solution into coarse scale problem and then obtains the coarse scale solution numerically. In the following, the brief introduction of VMEFG is presented and more details about the VMEFG can refer to [10,11].…”

Section: The Variational Multiscale Element Free Galerkin Methodsmentioning

confidence: 99%

“…A detailed review on the meshless methods has been provided by Nguyen et al [1] and Liu and Gu [2]. Recently many meshless methods have been proposed and applied to computational fluid dynamics [3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…VMEFG method inherits the advantages of the VMFEM, that is, it allows equal order basis for pressure and velocity and the stabilized parameter appear naturally. Subsequently, Zhang et al applied VMEFG to simulate the water wave problems [11] and MHD flow problems [12]. To the best of our knowledge, there are few published results when meshless method is used to non-Newtonian fluid flow problems and meshless method for the simulation of non-Newtonian are usually applied in collocation sets [13,14].…”

Section: Introductionmentioning

confidence: 99%

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The variational multiscale element free Galerkin method for the simulation of power-law fluid flows

Zhang¹,

Zhang²

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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In this work, the variational multiscale element free Galerkin method is used for the solution of incompressible generalized Newtonian fluid flow. In order to correct the lack of stability of the standard Galerkin formulation of the NavierStokes equations, the velocity field is decomposed into coarse and fine scales first, and then a model for the fine scale velocity is introduced, in the process, the stabilization parameter has appeared naturally via the solution of the fine scale problem. From the viewpoint of the application, the presented method can employ an equal order basis for pressure and velocity that is easy to implement but avoid the restriction of the Babuska-Brezzi condition. Two benchmark problems named Poiseuille flow and lid-driven cavity flow for the power-law are solved and the numerical results confirm that this method has better stability and accuracy.

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Section: Review Of the Element Free Galerkin Methodsmentioning

confidence: 99%

Section: The Variational Multiscale Element Free Galerkin Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The variational multiscale element free Galerkin method for the simulation of power-law fluid flows

Zhang¹,

Zhang²

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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show abstract

“…Employing this method, Masud and coworkers developed stabilized formulations for the Darcy flow (Masud and Hughes 2002), the convective-diffusive heat transfer (Ayub and Masud 2003), the advection-diffusion problems (Masud and Khurram 2004), and the incompressible flow problems (Masud and Khurram 2006). Extending this idea to the meshfree method, Zhang et al (2008Zhang et al ( , 2011b presented the variational multiscale elementfree Galerkin (VMEFG) method to overcome the numerical instabilities of the EFG method, which was introduced into the schemes coupling continuum and MD (Zhang et al 2011a).…”

Section: Introductionmentioning

confidence: 99%