Numerical Analysis of Thermo-electrically Conducting Fluids in a Cubic Cavity Using Vector Finite Element Method for Induction Equations

Matsumoto, Masaaki; Tanahashi, Takahiko

doi:10.2355/isijinternational.43.932

Cited by 2 publications

(3 citation statements)

References 7 publications

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“…These results prove that the developed numerical scheme is robust even when it is applied to an MHD natural convection problem (as well as an isothermal flow problem). The numerical solutions shown in Figures and agree well with those in Reference .…”

Section: Numerical Examplessupporting

confidence: 84%

“…This is a big advantage over some conventional approaches in which the electromagnetic field equations are also discretized by node‐based finite element methods , because iterative calculation is not required for satisfying the solenoidal condition. The idea of employing a vector finite element method for the analysis of MHD fluid flows was previously proposed in Reference . However, in that previous work, the velocity is interpolated using piecewise bilinear interpolation functions, and the accuracy of the numerical solutions on distorted meshes is not so high because of less accurate approximation procedures for the calculation of the integrals over the four‐node elements.…”

Section: Introductionmentioning

confidence: 99%

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A mixed‐interpolation finite element method for incompressible thermal flows of electrically conducting fluids

Kohno

2016

Numerical Methods in Fluids

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Summary A new mixed‐interpolation finite element method is presented for the two‐dimensional numerical simulation of incompressible magnetohydrodynamic (MHD) flows which involve convective heat transfer. The proposed method applies the nodal shape functions, which are locally defined in nine‐node elements, for the discretization of the Navier–Stokes and energy equations, and the vector shape functions, which are locally defined in four‐node elements, for the discretization of the electromagnetic field equations. The use of the vector shape functions allows the solenoidal condition on the magnetic field to be automatically satisfied in each four‐node element. In addition, efficient approximation procedures for the calculation of the integrals in the discretized equations are adopted to achieve high‐speed computation. With the use of the proposed numerical scheme, MHD channel flow and MHD natural convection under a constant applied magnetic field are simulated at different Hartmann numbers. The accuracy and robustness of the method are verified through these numerical tests in which both undistorted and distorted meshes are employed for comparison of numerical solutions. Furthermore, it is shown that the calculation speed for the proposed scheme is much higher compared with that for a conventional numerical integration scheme under the condition of almost the same memory consumption. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Numerical Examplessupporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

A mixed‐interpolation finite element method for incompressible thermal flows of electrically conducting fluids

Kohno

2016

Numerical Methods in Fluids

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“…一方，電磁場の空間の離散化には辺要素有限要素法 (Bíró, 1999;Matsumoto and Tanahashi, 2003)を用いる．こ (Fujiwara et al, 1996) ．そのため，本研究においても共役勾配法系統の解法を用いて解析を行う．式 (28) ～ (30) …”

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Three-dimensional numerical analysis of magnetohydrodynamic flow bounded by conducting walls under alternating-current magnetic fields

Mure

Kohno

2018

Transactions of the JSME (In Japanese)

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Three-dimensional (3D) numerical simulation of incompressible, magnetohydrodynamic (MHD) flows under alternating-current (AC) magnetic fields are carried out, which takes into account the coupling with the electromagnetic fields in the solid and gas regions. A numerical scheme is constructed by combining the Galerkin finite element method and the edge-element based finite element method, which are applied to the discretizations of the Navier-Stokes equations and the electromagnetic field equations, respectively. The solution algorithm for fluid flow is based on an explicit fractional step approach and the simultaneous relaxation of velocity and pressure to satisfy the continuity equation. The electromagnetic field equations are formulated with the use of the magnetic vector potential which is defined on the edge elements. In the proposed numerical scheme, the advection term in the induction equation is not neglected, because the scheme needs to deal with the condition where the advection term is the same order with the diffusion term in that equation. The validity of the numerical scheme is verified through the analysis of the electromagnetic field under a direct-current magnetic field, and numerical simulations of the MHD flows under spatially uniform AC magnetic fields are carried out. It is confirmed that the spatio-temporal mean Lorentz force in the conducting fluid becomes weaker with the increase in the dimensionless frequency due to the skin effect. It is also shown that the flow pattern in a hexahedral closed domain is largely changed when the frequency is getting higher, which is associated with the change in the Lorentz force profile.

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Numerical Analysis of Thermo-electrically Conducting Fluids in a Cubic Cavity Using Vector Finite Element Method for Induction Equations

Cited by 2 publications

References 7 publications

A mixed‐interpolation finite element method for incompressible thermal flows of electrically conducting fluids

A mixed‐interpolation finite element method for incompressible thermal flows of electrically conducting fluids

Three-dimensional numerical analysis of magnetohydrodynamic flow bounded by conducting walls under alternating-current magnetic fields

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