A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations

Shakeri, Fatemeh; Dehghan, Mehdi

doi:10.1016/j.apnum.2010.07.010

Cited by 75 publications

(30 citation statements)

References 86 publications

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“…The numerical analysis of heat transfer [10][11][12][13][14] has been independently, though not exclusively, developed in four main streams: the finite difference method (FDM) [15,16], the finite volume method (FVM) [17], the finite element method (FEM) [18][19][20], and the boundary element method (BEM) [21][22][23]. The FDM is based on using Taylor series expansion to find approximation formulas for derivative operators.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

Sârbu

Iosif

2017

Computation

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Abstract:The dual reciprocity method (DRM) is a highly efficient numerical method of transforming domain integrals arising from the non-homogeneous term of the Poisson equation into equivalent boundary integrals. In this paper, the velocity and temperature fields of laminar forced heat convection in a concentric annular tube, with constant heat flux boundary conditions, have been studied using numerical simulations. The DRM has been used to solve the governing equation, which is expressed in the form of a Poisson equation. A test problem is employed to verify the DRM solutions with different boundary element discretizations and numbers of internal points. The results of the numerical simulations are discussed and compared with exact analytical solutions. Good agreement between the numerical results and exact solutions is evident, as the maximum relative errors are less than 5% to 6%, and the R 2 -values are greater than 0.999 in all cases. These results confirm the effectiveness and accuracy of the proposed numerical model, which is based on the DRM.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

Sârbu

Iosif

2017

Computation

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“…This figure shows that the present method converges to the solution at an exponential rate. The interested reader can also see [51][52][53][54][55][56][57][58].…”

Section: Resultsmentioning

confidence: 98%

The use of Sinc‐collocation method for solving Falkner–Skan boundary‐layer equation

Parand

Dehghan

Pirkhedri

2010

Numerical Methods in Fluids

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SUMMARYThe MHD Falkner-Skan equation arises in the study of laminar boundary layers exhibiting similarity on the semi-infinite domain. The proposed approach is equipped by the orthogonal Sinc functions that have perfect properties. This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, the governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by the Sinc-collocation method. It is shown that the Sinc-collocation method converges to the solution at an exponential rate.

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“…The MHD flow problem may obtain analytical solution in some special conditions, but it can only be solved numerically in the general situation . In the past several decades, various numerical approximation methods, involving finite element method (FEM) [14][15][16][17][18][19][20][21][22][23], finite difference method (FDM) [7][8][9][10], boundary element method (BEM) [4][5][6], differential quadrature method (DQM) [24], meshfree (meshless) method (MM) [1][2][3], finite volume spectral element method (FVSEM) [25], have been suggested to solve the coupled equations in velocity and magnetic field for the steady magnetohydrodynamic (MHD) duct flow. However, most of them cannot solve the MHD problems with high Ha effectively.…”

Section: Introductionmentioning

confidence: 99%

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

Zhou

Tian

2015

Computer Physics Communications

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A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations

Cited by 75 publications

References 86 publications

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

Numerical Simulation of the Laminar Forced Convective Heat Transfer between Two Concentric Cylinders

The use of Sinc‐collocation method for solving Falkner–Skan boundary‐layer equation

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

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