Numerical Modeling of Stokes Flow in a Circular Cavity by Variational Multiscale Element Free Galerkin Method

Zhang, Ping; Zhang, Xiaohua

doi:10.1155/2014/451546

Cited by 7 publications

(5 citation statements)

References 23 publications

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“…Fig. 16 shows the distributions of velocity components u, v and pressure P. All the quantities are smoothly obtained at each DP, and the velocity components are in good agreement with those solved using a well-validated numerical method (Zhang and Zhang, 2014). For the sake of visualization, the boundary pressure is extrapolated from the obtained discrete pressures inside the domain using the MLS reconstruction described in Appendix A.…”

Section: Circular Couette Flowmentioning

confidence: 58%

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

MATSUDA

TSUKUI

2022

Mechanical Engineering Journal

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Meshless methods inherently do not require mesh topologies and are practically used for solving continuum equations. However, these methods generally tend to have a higher computational load than conventional mesh-based methods because calculation stencils for spatial discretization become large. In this study, a novel approach for the use of compact stencils in meshless methods is proposed, called the mesh-constrained discrete point (MCD) approach. The MCD approach introduces a Cartesian mesh system to the background of a domain. And the approach rigorously constrains the distribution of discrete points (DPs) in each mesh by solving a dynamic problem with nonlinear constraints. This can avoid the heterogeneity of the DP distribution at the mesh-size level and impose compact stencils with a fixed degree of freedom for derivative evaluations. A fundamental formulation for arrangements of DPs and an application to unsteady Stokes flows are presented in this paper. Numerical tests were performed for the distribution of DPs and flow problems in co-axial and eccentric circular channels. The proposed MCD approach achieved a reasonable distribution of DPs independently of the spatial resolution with a few iterations in pre-processing. Additionally, solutions using the obtained DP distributions in Stokes flow problems were in good agreement with theoretical and reference solutions. The results also confirmed that the numerical accuracies of velocity and pressure achieved the expected convergence order, even when compact stencils were used.

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Section: Circular Couette Flowmentioning

confidence: 58%

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

MATSUDA

TSUKUI

2022

Mechanical Engineering Journal

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“…The development of the EFG method continues to be carried out significantly to increase its accuracy; Zhang et al [12][13][14] developed the multiscale EFG method. This method divides the numerical solution into two parts, namely the global level solution and the local level solution.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Natural Convection Problems Using Radial Point Interpolation Meshless (RPIM) Method Combined with Artificial-Compressibility Model

Pranowo,

Santoso,

Wijayanta

2024

MCA

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A numerical method is used to solve the thermal analysis of natural convection in enclosures. This paper proposes the use of an implicit artificial-compressibility model in conjunction with the Radial Point Interpolation Meshless (RPIM) method to mimic laminar natural convective heat transport. The technique couples the pressure with the velocity components using an artificial compressibility model. The RPIM is used to discretize the spatial terms of the governing equation. We solve the semi-algebraic system implicitly in backward Euler pseudo-time. The proposed method solves two test problems—natural convection in the annulus of concentric circular cylinders and trapezoidal cavity. Additionally, the results are validated using experimental and numerical data available in the literature. Excellent agreement was seen between the numerical results acquired with the suggested method and those obtained through the standard techniques found in the literature.

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“…The incompressible Navier‐Stokes equation has been solved by meshless methods such as the MLS reproducing Kernel technique, the meshfree local Petrov‐Galerkin procedure, RBFs collocation method, meshless LRBFs method, the reduced‐order model based on the POD idea, a novel nonintrusive model reduction method, the VMEFG method, the 3D plate problem based on DQ approach, a novel vector‐potential formulation, approximate particular solutions, a novel immersed object method, boundary elements method combined with a finite difference procedure, and so on. Author of developed a new approach for solving MHD equation with high Hartmann numbers.…”

Section: Introductionmentioning

confidence: 99%

A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

Abbaszadeh

Dehghan

Navon

2020

Numerical Methods in Fluids

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Summary In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element‐free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced‐order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced‐order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two‐dimensional cases.

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Numerical Modeling of Stokes Flow in a Circular Cavity by Variational Multiscale Element Free Galerkin Method

Cited by 7 publications

References 23 publications

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

A particle-based method using the mesh-constrained discrete point approach for two-dimensional Stokes flows

Numerical Solution of Natural Convection Problems Using Radial Point Interpolation Meshless (RPIM) Method Combined with Artificial-Compressibility Model

A proper orthogonal decomposition variational multiscale meshless interpolating element‐free Galerkin method for incompressible magnetohydrodynamics flow

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