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Volumn 61, Issue 1, 2011, Pages 1-23

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

Author keywords

Finite volume method; Hermit interpolation; Rectangular mesh; Spectral element method; Triangular mesh; Unsteady magnetohydrodynamic equations

Indexed keywords

HERMIT INTERPOLATION; RECTANGULAR MESH; SPECTRAL ELEMENT METHOD; TRIANGULAR MESHES; UNSTEADY MAGNETOHYDRODYNAMIC EQUATIONS;

EID: 78049468429     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2010.07.010     Document Type: Article
Times cited : (75)

References (99)
  • 1
    • 0001075210 scopus 로고
    • Existence of electromagnetic-hydrodynamic waves
    • H. Alfvén Existence of electromagnetic-hydrodynamic waves Nature 150 1942 405 406
    • (1942) Nature , vol.150 , pp. 405-406
    • Alfvén, H.1
  • 2
    • 0037055457 scopus 로고    scopus 로고
    • A finite volume approach for unsteady viscoelastic fluid flows
    • H. Al Moatassime, and D. Esselaoui A finite volume approach for unsteady viscoelastic fluid flows Int. J. Numer. Meth. Fluid 39 2002 939 959
    • (2002) Int. J. Numer. Meth. Fluid , vol.39 , pp. 939-959
    • Al Moatassime, H.1    Esselaoui, D.2
  • 4
    • 0035050579 scopus 로고    scopus 로고
    • Duct flow with a transverse magnetic field at high Hartmann numbers
    • K.E. Barrett Duct flow with a transverse magnetic field at high Hartmann numbers Int. J. Numer. Meth. Eng. 50 2001 1893 1906
    • (2001) Int. J. Numer. Meth. Eng. , vol.50 , pp. 1893-1906
    • Barrett, K.E.1
  • 5
    • 0004058410 scopus 로고
    • Aspects of Unstructured Grids and Finite Volume Solvers for the Euler and Navier-Stokes Equations
    • Von Karman Institute
    • T. Barth Aspects of Unstructured Grids and Finite Volume Solvers for the Euler and Navier-Stokes Equations 25th Computational Fluid Dynamics Lecture Series 1994 Von Karman Institute
    • (1994) 25th Computational Fluid Dynamics Lecture Series
    • Barth, T.1
  • 6
    • 0017475628 scopus 로고
    • MHD flows due to current spreading in an axisymmetric layer of finite thickness
    • V. Bojarevics, and V.I. Sharamkin MHD flows due to current spreading in an axisymmetric layer of finite thickness Magnetohydrodynamics 13 1977 172 177
    • (1977) Magnetohydrodynamics , vol.13 , pp. 172-177
    • Bojarevics, V.1    Sharamkin, V.I.2
  • 7
    • 78049479666 scopus 로고
    • Magnetohydrodynamic interface waves and the distribution of heart caused by the dynamic interaction of currents in an aluminium electrolyte cell
    • V. Bojarevics Magnetohydrodynamic interface waves and the distribution of heart caused by the dynamic interaction of currents in an aluminium electrolyte cell Magnetohydrodynamics 28 1992 360 367
    • (1992) Magnetohydrodynamics , vol.28 , pp. 360-367
    • Bojarevics, V.1
  • 9
    • 33745307736 scopus 로고    scopus 로고
    • Comparison of MHD models for aluminium reduction cells
    • V. Bojarevics, and K. Pericleous Comparison of MHD models for aluminium reduction cells Light Metals 2 2006 347 352
    • (2006) Light Metals , vol.2 , pp. 347-352
    • Bojarevics, V.1    Pericleous, K.2
  • 10
    • 41449083084 scopus 로고    scopus 로고
    • Time-domain BEM solution of convection-diffusion-type MHD equations
    • N. Bozkaya, and M. Tezer-Sezgin Time-domain BEM solution of convection-diffusion-type MHD equations Int. J. Numer. Meth. Fluids 56 2008 1969 1991
    • (2008) Int. J. Numer. Meth. Fluids , vol.56 , pp. 1969-1991
    • Bozkaya, N.1    Tezer-Sezgin, M.2
  • 12
    • 0001063435 scopus 로고
    • On the finite volume element method
    • Z. Cai On the finite volume element method Numer. Math. 58 1991 713 735
    • (1991) Numer. Math. , vol.58 , pp. 713-735
    • Cai, Z.1
  • 13
    • 0026138971 scopus 로고
    • The finite volume element method for diffusion equations on general triangulations
    • Z. Cai, J. Mandel, and S. McCormick The finite volume element method for diffusion equations on general triangulations SIAM J. Numer. Anal. 28 2 1991 392 402
    • (1991) SIAM J. Numer. Anal. , vol.28 , Issue.2 , pp. 392-402
    • Cai, Z.1    Mandel, J.2    McCormick, S.3
  • 15
    • 0034155322 scopus 로고    scopus 로고
    • Second-order finite-volume schemes for a non-linear hyperbolic equation: Error estimate
    • C. Chainais-Hillairet Second-order finite-volume schemes for a non-linear hyperbolic equation: Error estimate Math. Method. Appl. Sci. 23 2000 467 490
    • (2000) Math. Method. Appl. Sci. , vol.23 , pp. 467-490
    • Chainais-Hillairet, C.1
  • 16
    • 0033555206 scopus 로고    scopus 로고
    • Solution of incompressible flows with or without a free surface using the finite volume method on unstructured triangular meshes
    • C.T. Chan, and K. Anastasiou Solution of incompressible flows with or without a free surface using the finite volume method on unstructured triangular meshes Int. J. Numer. Meth. Fluids 29 1999 35 57
    • (1999) Int. J. Numer. Meth. Fluids , vol.29 , pp. 35-57
    • Chan, C.T.1    Anastasiou, K.2
  • 17
    • 0002408243 scopus 로고
    • Duct flow in magnetohydrodynamics
    • C.C. Chang, and T.S. Lundgren Duct flow in magnetohydrodynamics ZAMP 12 1961 100 114
    • (1961) ZAMP , vol.12 , pp. 100-114
    • Chang, C.C.1    Lundgren, T.S.2
  • 18
    • 0033432593 scopus 로고    scopus 로고
    • A finite volume method based on the Crouzeix-Raviart element for elliptic PDE's in two dimensions
    • P. Chatzipantelidis A finite volume method based on the Crouzeix-Raviart element for elliptic PDE's in two dimensions Numer. Math. 82 1999 409 432
    • (1999) Numer. Math. , vol.82 , pp. 409-432
    • Chatzipantelidis, P.1
  • 19
    • 4444381362 scopus 로고    scopus 로고
    • Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
    • P. Chatzipantelidis, R.D. Lazarov, and V. Thomée Error estimates for a finite volume element method for parabolic equations in convex polygonal domains Numer. Meth. Partial Differential Eq. 20 2004 650 674
    • (2004) Numer. Meth. Partial Differential Eq. , vol.20 , pp. 650-674
    • Chatzipantelidis, P.1    Lazarov, R.D.2    Thomée, V.3
  • 22
    • 61549088742 scopus 로고    scopus 로고
    • Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
    • M. Dehghan, and D. Mirzaei Meshless Local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity Appl. Numer. Math. 59 2009 1043 1058
    • (2009) Appl. Numer. Math. , vol.59 , pp. 1043-1058
    • Dehghan, M.1    Mirzaei, D.2
  • 23
    • 68849115222 scopus 로고    scopus 로고
    • Meshless local boundary integral equation (LBIE) method for the unsteady magnetohydrodynamic (MHD) flow in rectangular and circular pipes
    • M. Dehghan, and D. Mirzaei Meshless local boundary integral equation (LBIE) method for the unsteady magnetohydrodynamic (MHD) flow in rectangular and circular pipes Comput. Phys. Commun. 180 2009 1458 1466
    • (2009) Comput. Phys. Commun. , vol.180 , pp. 1458-1466
    • Dehghan, M.1    Mirzaei, D.2
  • 24
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
    • M. Dehghan Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices Math. Comput. Simulation 71 2006 16 30
    • (2006) Math. Comput. Simulation , vol.71 , pp. 16-30
    • Dehghan, M.1
  • 25
    • 11144275388 scopus 로고    scopus 로고
    • On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation
    • M. Dehghan On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation Numer. Methods Partial Differential Eq. 21 2005 24 40
    • (2005) Numer. Methods Partial Differential Eq. , vol.21 , pp. 24-40
    • Dehghan, M.1
  • 26
    • 0031335764 scopus 로고    scopus 로고
    • A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers
    • Z. Demendy, T. Nagy, and M.-E. Hungary A new algorithm for solution of equations of MHD channel flows at moderate Hartmann numbers Acta Mech. 123 1997 135 149
    • (1997) Acta Mech. , vol.123 , pp. 135-149
    • Demendy, Z.1    Nagy, T.2    Hungary, M.-E.3
  • 28
    • 0037059199 scopus 로고    scopus 로고
    • Performance of finite volume solutions to the shallow water equations with shock-capturing schemes
    • K.S. Erduran, V. Kutija, and C.J.M. Hewett Performance of finite volume solutions to the shallow water equations with shock-capturing schemes Int. J. Numer. Meth. Fluids 40 2002 1237 1273
    • (2002) Int. J. Numer. Meth. Fluids , vol.40 , pp. 1237-1273
    • Erduran, K.S.1    Kutija, V.2    Hewett, C.J.M.3
  • 29
    • 0141716196 scopus 로고    scopus 로고
    • Finite volume element approximations of nonlocal in time one-dimensional flows in porous media
    • R.E. Ewing, R.D. Lazarov, and Y. Lin Finite volume element approximations of nonlocal in time one-dimensional flows in porous media Computing 64 2000 157 182
    • (2000) Computing , vol.64 , pp. 157-182
    • Ewing, R.E.1    Lazarov, R.D.2    Lin, Y.3
  • 30
    • 0036556364 scopus 로고    scopus 로고
    • On the accuracy of the finite volume element method based on piecewise linear polynomials
    • R.E. Ewing, T. Lin, and Y. Lin On the accuracy of the finite volume element method based on piecewise linear polynomials SIAM J. Numer. Anal. 39 6 2002 1865 1888
    • (2002) SIAM J. Numer. Anal. , vol.39 , Issue.6 , pp. 1865-1888
    • Ewing, R.E.1    Lin, T.2    Lin, Y.3
  • 32
    • 57649129177 scopus 로고    scopus 로고
    • Splitting based finite volume schemes for ideal MHD equations
    • F.G. Fuchs, S. Mishra, and N.H. Risebro Splitting based finite volume schemes for ideal MHD equations J. Comput. Phys. 228 2009 641 660
    • (2009) J. Comput. Phys. , vol.228 , pp. 641-660
    • Fuchs, F.G.1    Mishra, S.2    Risebro, N.H.3
  • 33
    • 0029347382 scopus 로고
    • A two-dimensional bi-cubic B-spline finite element used in a study of MHD duct flow
    • L.R.T. Gardner, and G.A. Gardner A two-dimensional bi-cubic B-spline finite element used in a study of MHD duct flow Comput. Methods Appl. Mech. Engrg. 124 1995 365 375
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.124 , pp. 365-375
    • Gardner, L.R.T.1    Gardner, G.A.2
  • 34
    • 84950658093 scopus 로고
    • Magnetohydrodynamic pipe flow. Part 1
    • R.R. Gold Magnetohydrodynamic pipe flow. Part 1 J. Fluid Mech. 13 1962 505 512
    • (1962) J. Fluid Mech. , vol.13 , pp. 505-512
    • Gold, R.R.1
  • 35
    • 33846146338 scopus 로고    scopus 로고
    • An interior penalty Galerkin method for the MHD equations in heterogeneous domains
    • J.L. Guermond, R. Laguerre, J. Léorat, and C. Nore An interior penalty Galerkin method for the MHD equations in heterogeneous domains J. Comput. Phys. 221 2007 349 369
    • (2007) J. Comput. Phys. , vol.221 , pp. 349-369
    • Guermond, J.L.1    Laguerre, R.2    Léorat, J.3    Nore, C.4
  • 36
    • 33845602193 scopus 로고    scopus 로고
    • An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
    • J. Han, and H. Tang An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics J. Comput. Phys. 220 2007 791 812
    • (2007) J. Comput. Phys. , vol.220 , pp. 791-812
    • Han, J.1    Tang, H.2
  • 37
    • 0010889577 scopus 로고
    • Theory of the laminar flow of an electrically conducting liquid in a homogeneous magnetic field
    • J. Hartmann, and I. Hg-Dynamics Theory of the laminar flow of an electrically conducting liquid in a homogeneous magnetic field K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 15 1937 1 27
    • (1937) K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. , vol.15 , pp. 1-27
    • Hartmann, J.1    Hg-Dynamics, I.2
  • 38
    • 69049111663 scopus 로고    scopus 로고
    • High-order adaptive quadrature-free spectral volume method on unstructured grids
    • R.E. Harris, and Z.J. Wang High-order adaptive quadrature-free spectral volume method on unstructured grids Computers and Fluids 38 2009 2006 2025
    • (2009) Computers and Fluids , vol.38 , pp. 2006-2025
    • Harris, R.E.1    Wang, Z.J.2
  • 39
    • 78049459330 scopus 로고
    • A review of MHD flows in ducts with changing cross section areas and non-uniform magnetic fields
    • E.T. Holroyd, and J.C.R. Hunt A review of MHD flows in ducts with changing cross section areas and non-uniform magnetic fields Euromech Colloquium 70 1976 16 19
    • (1976) Euromech Colloquium , vol.70 , pp. 16-19
    • Holroyd, E.T.1    Hunt, J.C.R.2
  • 40
    • 2742536946 scopus 로고
    • An experimental study of the effects of wall conductivity, non-uniform magnetic field and variable-area ducts on liquid metal flow at high Hartmann number, Part 1: Ducts with non-conducting walls
    • R.J. Holroyd An experimental study of the effects of wall conductivity, non-uniform magnetic field and variable-area ducts on liquid metal flow at high Hartmann number, Part 1: Ducts with non-conducting walls J. Fluid Mech. 93 1979 609 630
    • (1979) J. Fluid Mech. , vol.93 , pp. 609-630
    • Holroyd, R.J.1
  • 41
    • 0018916156 scopus 로고
    • MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field
    • R.J. Holroyd MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field J. Fluid Mech. 96 1980 335 353
    • (1980) J. Fluid Mech. , vol.96 , pp. 335-353
    • Holroyd, R.J.1
  • 42
    • 0024933742 scopus 로고
    • Three-dimensional MHD flow in insulating circular ducts in non-uniform transverse magnetic fields
    • T.Q. Hua, and J.S. Walker Three-dimensional MHD flow in insulating circular ducts in non-uniform transverse magnetic fields Int. J. Engrg. Sci. 27 1989 1079 1091
    • (1989) Int. J. Engrg. Sci. , vol.27 , pp. 1079-1091
    • Hua, T.Q.1    Walker, J.S.2
  • 44
    • 0020982482 scopus 로고
    • A quasi one dimensional analysis of an electromagnetic pump including end effects
    • W.F. Hughes, and I.R. McNAB A quasi one dimensional analysis of an electromagnetic pump including end effects H. Branover, P.S. Lykoudis, A. Yakhot, Liquid-Metal Flows and Magnetohydrodynamics Progress in Astronautics and Aeronautics 84 1983 287 312
    • (1983) Progress in Astronautics and Aeronautics , vol.84 , pp. 287-312
    • Hughes, W.F.1    McNab, I.R.2
  • 45
    • 0028388994 scopus 로고
    • The CFD analysis of simple parabolic and elliptic MHD flows
    • M. Hughes, K.A. Pericleous, and M. Cross The CFD analysis of simple parabolic and elliptic MHD flows Appl. Math. Modelling 18 1994 150 155
    • (1994) Appl. Math. Modelling , vol.18 , pp. 150-155
    • Hughes, M.1    Pericleous, K.A.2    Cross, M.3
  • 46
    • 0029502493 scopus 로고
    • The numerical modelling of DC electromagnetic pump and brake flow
    • M. Hughes, K.A. Pericleous, and M. Cross The numerical modelling of DC electromagnetic pump and brake flow Appl. Math. Model. 19 1995 713 723
    • (1995) Appl. Math. Model. , vol.19 , pp. 713-723
    • Hughes, M.1    Pericleous, K.A.2    Cross, M.3
  • 47
    • 0001178257 scopus 로고    scopus 로고
    • On the finite volume element method for general self-adjoint elliptic problems
    • J.G. Huang, and S.T. Xi On the finite volume element method for general self-adjoint elliptic problems SIAM J. Numer. Anal. 35 1998 1762 1774
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1762-1774
    • Huang, J.G.1    Xi, S.T.2
  • 48
    • 67349160588 scopus 로고
    • Magnetohydrodynamic flow in rectangular ducts
    • J.C.R. Hunt Magnetohydrodynamic flow in rectangular ducts J. Fluid Mech. 21 1965 577 590
    • (1965) J. Fluid Mech. , vol.21 , pp. 577-590
    • Hunt, J.C.R.1
  • 50
    • 0002300333 scopus 로고
    • Analysis of locally stabilized mixed finite element methods for the Stokes problem
    • N. Kechkar, and D. Silvester Analysis of locally stabilized mixed finite element methods for the Stokes problem Math. Comput. 58 1992 1 10
    • (1992) Math. Comput. , vol.58 , pp. 1-10
    • Kechkar, N.1    Silvester, D.2
  • 53
    • 16344371088 scopus 로고    scopus 로고
    • Well-balanced finite volume evolution Galerkin methods for the shallow water equations with source terms
    • M. Lukáčová-Medvid'ová, and Z. Vlk Well-balanced finite volume evolution Galerkin methods for the shallow water equations with source terms Int. J. Numer. Meth. Fluids 47 2005 1165 1171
    • (2005) Int. J. Numer. Meth. Fluids , vol.47 , pp. 1165-1171
    • Lukáčová-Medvid'Ová, M.1    Vlk, Z.2
  • 54
    • 38249000618 scopus 로고
    • Finite element analysis of magnetohydrodynamic pipe flow
    • A.J. Meir Finite element analysis of magnetohydrodynamic pipe flow Appl. Math. Comput. 57 1993 177 196
    • (1993) Appl. Math. Comput. , vol.57 , pp. 177-196
    • Meir, A.J.1
  • 55
    • 0000002483 scopus 로고    scopus 로고
    • Analysis and numerical approximation of a stationary MHD flow problem with nonideal boundary
    • A.J. Meir, and P.G. Schmidt Analysis and numerical approximation of a stationary MHD flow problem with nonideal boundary SIAM J. Numer. Anal. 36 1999 1304 1332
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1304-1332
    • Meir, A.J.1    Schmidt, P.G.2
  • 56
    • 34547539883 scopus 로고    scopus 로고
    • A simple and accurate Riemann solver for isothermal MHD
    • A. Mignone A simple and accurate Riemann solver for isothermal MHD J. Comput. Phys. 225 2007 1427 1441
    • (2007) J. Comput. Phys. , vol.225 , pp. 1427-1441
    • Mignone, A.1
  • 57
    • 0001721512 scopus 로고
    • Optimal multilevel iterative methods for adaptive grids
    • W.R. Mitchell Optimal multilevel iterative methods for adaptive grids SIAM J. Sci. Stat. Comp. 13 1992 146 167
    • (1992) SIAM J. Sci. Stat. Comp. , vol.13 , pp. 146-167
    • Mitchell, W.R.1
  • 58
  • 59
    • 33646111183 scopus 로고    scopus 로고
    • Finite element method solution of electrically driven magnetohydrodynamic flow
    • A.I. Neslitürk, and M. Tezer-Sezgin Finite element method solution of electrically driven magnetohydrodynamic flow J. Comput. Appl. Math. 192 2006 339 352
    • (2006) J. Comput. Appl. Math. , vol.192 , pp. 339-352
    • Neslitürk, A.I.1    Tezer-Sezgin, M.2
  • 60
    • 35348819989 scopus 로고    scopus 로고
    • A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number, Part 1: On a rectangular collocated grid system
    • M.J. Ni, R. Munipalli, N.B. Morley, P. Huang, and M.A. Abdou A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number, Part 1: On a rectangular collocated grid system J. Comput. Phys. 227 2007 174 204
    • (2007) J. Comput. Phys. , vol.227 , pp. 174-204
    • Ni, M.J.1    Munipalli, R.2    Morley, N.B.3    Huang, P.4    Abdou, M.A.5
  • 61
    • 0000587135 scopus 로고    scopus 로고
    • On the numerical implementation of nonlinear viscoelastic models in a finite-volume method
    • P.J. Oliveira On the numerical implementation of nonlinear viscoelastic models in a finite-volume method Numer. Heat Transfer, Part B 40 2001 283 301
    • (2001) Numer. Heat Transfer, Part B , vol.40 , pp. 283-301
    • Oliveira, P.J.1
  • 62
    • 48549109395 scopus 로고
    • A spectral element method for fluid dynamics: Laminar flow in a channel expansion
    • A.T. Patera A spectral element method for fluid dynamics: Laminar flow in a channel expansion J. Comput. Phys. 54 1984 468 488
    • (1984) J. Comput. Phys. , vol.54 , pp. 468-488
    • Patera, A.T.1
  • 64
    • 34249785996 scopus 로고    scopus 로고
    • Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications
    • K.A. Pericleous, and V. Bojarevics Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications Progr. Comput. Fluid Dynam. 7 2007 118 127
    • (2007) Progr. Comput. Fluid Dynam. , vol.7 , pp. 118-127
    • Pericleous, K.A.1    Bojarevics, V.2
  • 65
    • 0028388994 scopus 로고
    • The CFD analysis of simple parabolic and elliptic MHD flows
    • K.A. Pericleous, M. Hughes, and M. Cross The CFD analysis of simple parabolic and elliptic MHD flows Appl. Math. Modelling 18 1994 150 155
    • (1994) Appl. Math. Modelling , vol.18 , pp. 150-155
    • Pericleous, K.A.1    Hughes, M.2    Cross, M.3
  • 66
    • 0001423178 scopus 로고
    • Magnetohydrodynamic channel flow study
    • J.I. Ramos, and N.S. Winowich Magnetohydrodynamic channel flow study Phys. Fluids 29 1986 992 997
    • (1986) Phys. Fluids , vol.29 , pp. 992-997
    • Ramos, J.I.1    Winowich, N.S.2
  • 67
    • 0025508299 scopus 로고
    • Finite difference and finite element methods for MHD channel flows
    • J.I. Ramos, and N.S. Winowich Finite difference and finite element methods for MHD channel flows Int. J. Numer. Meth. Fluids 11 1990 907 934
    • (1990) Int. J. Numer. Meth. Fluids , vol.11 , pp. 907-934
    • Ramos, J.I.1    Winowich, N.S.2
  • 68
    • 55649105407 scopus 로고    scopus 로고
    • Linear feedback control and approximation for a system governed by unsteady MHD equations
    • S.S. Ravindran Linear feedback control and approximation for a system governed by unsteady MHD equations Comput. Methods Appl. Mech. Engrg. 198 2008 524 541
    • (2008) Comput. Methods Appl. Mech. Engrg. , vol.198 , pp. 524-541
    • Ravindran, S.S.1
  • 69
    • 33749056084 scopus 로고    scopus 로고
    • A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
    • D.R. Reynolds, R. Samtaney, and C.S. Woodward A fully implicit numerical method for single-fluid resistive magnetohydrodynamics J. Comput. Phys. 219 2006 144 162
    • (2006) J. Comput. Phys. , vol.219 , pp. 144-162
    • Reynolds, D.R.1    Samtaney, R.2    Woodward, C.S.3
  • 71
    • 0026238362 scopus 로고
    • Magnetohydrodynamic steady flow computation in three dimensions
    • L. Seungsoo, and G.S. Dulikravich Magnetohydrodynamic steady flow computation in three dimensions Int. J. Numer. Meth. Fluids 13 1991 917 936
    • (1991) Int. J. Numer. Meth. Fluids , vol.13 , pp. 917-936
    • Seungsoo, L.1    Dulikravich, G.S.2
  • 72
    • 84938929392 scopus 로고
    • Steady motion of conducting fluids in pipes under transverse magnetic fields
    • J.A. Shercliff Steady motion of conducting fluids in pipes under transverse magnetic fields Proc. Camb. Phil. Soc. 49 1953 136 144
    • (1953) Proc. Camb. Phil. Soc. , vol.49 , pp. 136-144
    • Shercliff, J.A.1
  • 73
    • 3843104977 scopus 로고    scopus 로고
    • Development of a convection-diffusion-reaction magnetohydrodynamic solver on nonstaggered grids
    • T.W.H. Sheu, and R.K. Lin Development of a convection-diffusion-reaction magnetohydrodynamic solver on nonstaggered grids Int. J. Numer. Meth. Fluids 45 2004 1209 1233
    • (2004) Int. J. Numer. Meth. Fluids , vol.45 , pp. 1209-1233
    • Sheu, T.W.H.1    Lin, R.K.2
  • 74
    • 0242361534 scopus 로고
    • MHD axial flow in a triangular pipe under transverse magnetic field
    • B. Singh, and J. Lal MHD axial flow in a triangular pipe under transverse magnetic field Indian J. Pure Appl. Math. 9 1978 101 115
    • (1978) Indian J. Pure Appl. Math. , vol.9 , pp. 101-115
    • Singh, B.1    Lal, J.2
  • 75
    • 0018468747 scopus 로고
    • MHD axial flow in a triangular pipe under transverse magnetic field parallel to a side of the triangle
    • B. Singh, and J. Lal MHD axial flow in a triangular pipe under transverse magnetic field parallel to a side of the triangle Ind. J. Tech. 17 1979 184 189
    • (1979) Ind. J. Tech. , vol.17 , pp. 184-189
    • Singh, B.1    Lal, J.2
  • 76
    • 0020155397 scopus 로고
    • FEM in MHD channel flow problems
    • B. Singh, and J. Lal FEM in MHD channel flow problems Int. J. Numer. Meth. Eng. 18 1982 1104 1111
    • (1982) Int. J. Numer. Meth. Eng. , vol.18 , pp. 1104-1111
    • Singh, B.1    Lal, J.2
  • 77
    • 0020195380 scopus 로고
    • Heat transfer for MHD flow through a rectangular pipe with discontinuity in wall temperatures
    • B. Singh, and J. Lal Heat transfer for MHD flow through a rectangular pipe with discontinuity in wall temperatures J. Heat Moss Transfer 25 1982 1523 1529
    • (1982) J. Heat Moss Transfer , vol.25 , pp. 1523-1529
    • Singh, B.1    Lal, J.2
  • 78
    • 0021393983 scopus 로고
    • FEM for unsteady MHD flow through pipes with arbitrary wall conductivity
    • B. Singh, and J. Lal FEM for unsteady MHD flow through pipes with arbitrary wall conductivity Int. J. Numer. Meth. Fluids 4 1984 291 302
    • (1984) Int. J. Numer. Meth. Fluids , vol.4 , pp. 291-302
    • Singh, B.1    Lal, J.2
  • 79
    • 78049471545 scopus 로고
    • Finite element method for unsteady MHD channel flow with arbitrary wall conductivity and orientation of applied magnetic field
    • B. Singh, J. Lal, and P.K. Agarwal Finite element method for unsteady MHD channel flow with arbitrary wall conductivity and orientation of applied magnetic field Indian J. Pure Appl. Math. 16 11 1985 1390 1398
    • (1985) Indian J. Pure Appl. Math. , vol.16 , Issue.11 , pp. 1390-1398
    • Singh, B.1    Lal, J.2    Agarwal, P.K.3
  • 80
    • 0037298008 scopus 로고    scopus 로고
    • Dynamic solid mechanics using finite volume methods
    • A.K. Slone, C. Bailey, and M. Cross Dynamic solid mechanics using finite volume methods Appl. Math. Model. 27 2003 69 87
    • (2003) Appl. Math. Model. , vol.27 , pp. 69-87
    • Slone, A.K.1    Bailey, C.2    Cross, M.3
  • 81
    • 0015142729 scopus 로고
    • Some asymptotic extremum principles for magnetohydrodynamic pipe flow
    • P. Smith Some asymptotic extremum principles for magnetohydrodynamic pipe flow Appl. Sci. Res. 24 1971 452 466
    • (1971) Appl. Sci. Res. , vol.24 , pp. 452-466
    • Smith, P.1
  • 82
    • 0025459985 scopus 로고
    • Numerical simulation of liquid-metal MHD flows in rectangular ducts
    • A. Sterl Numerical simulation of liquid-metal MHD flows in rectangular ducts J. Fluid Mech. 216 1990 161 191
    • (1990) J. Fluid Mech. , vol.216 , pp. 161-191
    • Sterl, A.1
  • 83
    • 0032181582 scopus 로고    scopus 로고
    • The magnetic field and performance calculations for an electromagnetic pump of a liquid metal
    • C. Suwon, and H.H. Sang The magnetic field and performance calculations for an electromagnetic pump of a liquid metal J. Phys. D: Appl. Phys. 31 1998 2754 2759
    • (1998) J. Phys. D: Appl. Phys. , vol.31 , pp. 2754-2759
    • Suwon, C.1    Sang, H.H.2
  • 84
    • 0036170734 scopus 로고    scopus 로고
    • Unsteady MHD flow and heat transfer on a rotating disk in an ambient fluid
    • H.S. Takhar, A.K. Singh, and G. Nath Unsteady MHD flow and heat transfer on a rotating disk in an ambient fluid Int. J. Therm. Sci. 41 2002 147 155
    • (2002) Int. J. Therm. Sci. , vol.41 , pp. 147-155
    • Takhar, H.S.1    Singh, A.K.2    Nath, G.3
  • 85
    • 0023378616 scopus 로고    scopus 로고
    • Magnetohydrodynamic flow in a rectangular duct
    • M. Tezer-Sezgin Magnetohydrodynamic flow in a rectangular duct Int. J. Numer. Meth. Fluids 7 2005 697 718
    • (2005) Int. J. Numer. Meth. Fluids , vol.7 , pp. 697-718
    • Tezer-Sezgin, M.1
  • 86
    • 0036487025 scopus 로고    scopus 로고
    • Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions
    • M. Tezer-Sezgin, and S. Han AydIn Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions Int. J. Comput. Fluid Dyn. 16 1 2002 88 92
    • (2002) Int. J. Comput. Fluid Dyn. , vol.16 , Issue.1 , pp. 88-92
    • Tezer-Sezgin, M.1    Han Aydin, S.2
  • 87
    • 0024608898 scopus 로고
    • Finite element method for solving MHD flow in a rectangular duct
    • M. Tezer-Sezgin, and S. Köksal Finite element method for solving MHD flow in a rectangular duct Int. J. Numer. Meth. Eng. 28 1989 445 459
    • (1989) Int. J. Numer. Meth. Eng. , vol.28 , pp. 445-459
    • Tezer-Sezgin, M.1    Köksal, S.2
  • 91
    • 0016342576 scopus 로고
    • MHD flow in insulating circular expansions with strong transverse magnetic fields
    • J.S. Walker, and G.S.S. Ludford MHD flow in insulating circular expansions with strong transverse magnetic fields Int. J. Eng. Sci. 12 1974 1045 1061
    • (1974) Int. J. Eng. Sci. , vol.12 , pp. 1045-1061
    • Walker, J.S.1    Ludford, G.S.S.2
  • 92
    • 0037108398 scopus 로고    scopus 로고
    • Simulating the hydraulic characteristics of the lower Yellow River by the finite-volume technique
    • Q. Wan, H. Wan, C. Zhou, and Y. Wu Simulating the hydraulic characteristics of the lower Yellow River by the finite-volume technique Hydrol. Process. 16 2002 2767 2779
    • (2002) Hydrol. Process. , vol.16 , pp. 2767-2779
    • Wan, Q.1    Wan, H.2    Zhou, C.3    Wu, Y.4
  • 94
    • 40649125798 scopus 로고    scopus 로고
    • An unstructured finite volume approach for structural dynamics in response to fluid motions
    • G. Xia, and C.L. Lin An unstructured finite volume approach for structural dynamics in response to fluid motions Comput. Struct. 86 2008 684 701
    • (2008) Comput. Struct. , vol.86 , pp. 684-701
    • Xia, G.1    Lin, C.L.2
  • 95
    • 34447091911 scopus 로고    scopus 로고
    • Finite volume element method with interpolated coefficients for two-point boundary value problem of semilinear differential equations
    • Z. Xiong, and Y. Chen Finite volume element method with interpolated coefficients for two-point boundary value problem of semilinear differential equations Comput. Methods Appl. Mech. Engrg. 196 2007 3798 3804
    • (2007) Comput. Methods Appl. Mech. Engrg. , vol.196 , pp. 3798-3804
    • Xiong, Z.1    Chen, Y.2
  • 96
    • 0020152017 scopus 로고
    • Finite element analysis of magnetohydrodynamics and its application to lithium blanket design of fusion reactor
    • G. Yagawa, and M. Masuda Finite element analysis of magnetohydrodynamics and its application to lithium blanket design of fusion reactor Nucl. Eng. Design 71 1982 121 136
    • (1982) Nucl. Eng. Design , vol.71 , pp. 121-136
    • Yagawa, G.1    Masuda, M.2
  • 97
    • 34447272022 scopus 로고    scopus 로고
    • Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
    • H.C. Yee, and B. Sjögreen Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems J. Comput. Phys. 225 2007 910 934
    • (2007) J. Comput. Phys. , vol.225 , pp. 910-934
    • Yee, H.C.1    Sjögreen, B.2
  • 98
    • 33644957069 scopus 로고    scopus 로고
    • Solving the MHD equations by the space-time conservation element and solution element method
    • M. Zhang, S.T. John Yu, S.C. Henry Lin, S.C. Chang, and I. Blankson Solving the MHD equations by the space-time conservation element and solution element method J. Comput. Phys. 214 2006 599 617
    • (2006) J. Comput. Phys. , vol.214 , pp. 599-617
    • Zhang, M.1    John, T.Y.S.2    Henry, C.L.S.3    Chang, S.C.4    Blankson, I.5
  • 99
    • 34447536391 scopus 로고    scopus 로고
    • A finite volume solution of wave forces on submarine pipelines
    • Z.P. Zang, B. Teng, W. Bai, and L. Cheng A finite volume solution of wave forces on submarine pipelines Ocean Eng. 34 2007 1955 1964
    • (2007) Ocean Eng. , vol.34 , pp. 1955-1964
    • Zang, Z.P.1    Teng, B.2    Bai, W.3    Cheng, L.4


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