Local radial point interpolation method for the fully developed magnetohydrodynamic flow

Cai, Xinghui; Su, G.H.; Qiu, Suizheng

doi:10.1016/j.amc.2010.11.004

Cited by 18 publications

(6 citation statements)

References 36 publications

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“…The MHD model is simulated by meshless local Petrov‐Galerkin (MLPG) method, meshfree weak‐strong (MWS) form, local radial point interpolation method, boundary element method, finite difference method, finite element method, local point collocation method, the variational multiscale EFG method, and other numerical techniques …”

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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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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“…The boundary element method has been used extensively for solving MHD flow in ducts by Liu and Zhu, Hosseinzadeh et al, Tezer‐Sezgin and Bozkaya, and Tezer‐Sezgin and Han Aydın . Finite difference solution of MHD flow was given by Sheu and Lin, and some meshless method solutions are due to Dehghan and Mirzai, Loukopoulos et al, and Cai et al in channels for arbitrary cross section and arbitrary wall conductivities. Dehghan and Mohammadi and Dehghan and Salehi carried meshless methods based on radial basis functions as multiquadrics, inverse quadrics and Wendland function, and meshfree collocation method in strong form for essential boundary and meshless local Petrov‐Galerkin method in weak form for natural boundary, respectively.…”

Section: Introductionmentioning

confidence: 99%

Semi‐analytical solution of MHD flow through boundary integrals on the pipe wall

Tezer‐Sezgin

Bozkaya

2019

Math Methods in App Sciences

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A mathematical model is given for the magnetohydrodynamic (MHD) pipe flow as an inner Dirichlet problem in a 2D circular cross section of the pipe, coupled with an outer Dirichlet or Neumann magnetic problem. Inner Dirichlet problem is given as the coupled convection‐diffusion equations for the velocity and the induced current of the fluid coupling also to the outer problem, which is defined with the Laplace equation for the induced magnetic field of the exterior region with either Dirichlet or Neumann boundary condition. Unique solution of inner Dirichlet problem is obtained theoretically reducing it into two boundary integral equations defined on the boundary by using the corresponding fundamental solutions. Exterior solution is also given theoretically on the pipe wall with Poisson integral, and it is unique with Dirichlet boundary condition but exists with an additive constant obtained through coupled boundary and solvability conditions in Neumann wall condition. The collocation method is used to discretize these boundary integrals on the pipe wall. Thus, the proposed procedure is an improved theoretical analysis for combining the solution methods for the interior and exterior regions, which are consolidated numerically showing the flow behavior. The solution is simulated for several values of problem parameters, and the well‐known MHD characteristics are observed inside the pipe for increasing values of Hartmann number maintaining the continuity of induced currents on the pipe wall.

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“…The radial point interpolation method (RPIM), proposed in [21] and applied in [22] by JG Wang and GR Li, possess the Kronecker delta function properties, which is helpful to enforce the essential boundary conditions. However, RPIM could only simulate MHD flows [23] at lower magnetic field with Hartmann number less than 50 with out any modifications. We modified the two level element-free Galerkin method and proposed a two-level radial point interpolation method (TLRPIM) [24] to simulate MHD flow in a circular duct.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulations on the Fully Developed Liquid-metal MHD Flow at High Hartmann Numbers in the Rectangular Duct

Cai¹,

Hu²,

Dong³

et al. 2018

Proceedings of the 2018 2nd International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2018)

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Numerical simulation on the liquid metal mangetohydrodynamic (MHD) flow is a very attractive way to study the MHD flow problems. The two-level radial point interpolation method is applied to study the fully developed MHD flow in this work. With the method, numerical simulations of the MHD flows at Hartmann numbers up to 10 4 in a duct with arbitrary wall conductance ratios, namely, from thin conducting to insulated wall ducts, are conducted. The non-dimensional flowrate for different electrical conductivities of the duct wall are listed and compared with the exact solutions, showing a good accuracy. These results also indicate that the higher electrical conductivity of the duct wall, the lower non-dimensional flowrate, which is consistent with the well-known MHD flow behavior. Numerical simulations for insulated walls with conducting cracks or different orientation of external applied magnetic field are also carried out with the two-level radial point interpolation method.

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Local radial point interpolation method for the fully developed magnetohydrodynamic flow

Cited by 18 publications

References 36 publications

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

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

Semi‐analytical solution of MHD flow through boundary integrals on the pipe wall

Numerical Simulations on the Fully Developed Liquid-metal MHD Flow at High Hartmann Numbers in the Rectangular Duct

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