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Volumn 152, Issue 2, 1999, Pages 608-641

A Discontinuous Galerkin Method for the Viscous MHD Equations

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL EFFICIENCY; GALERKIN METHODS; JACOBIAN MATRICES; MAGNETOHYDRODYNAMICS; NUMERICAL METHODS; POLYNOMIALS;

EID: 0142160893     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6248     Document Type: Article
Times cited : (125)

References (43)
  • 1
    • 0003161948 scopus 로고
    • A simple Riemann solver and high-order Godunov schemes for hyperbolic systems of conservation laws
    • W. Dai and P. R. Woodward, A simple Riemann solver and high-order Godunov schemes for hyperbolic systems of conservation laws, J. Comput. Phys. 121, 51 (1995).
    • (1995) J. Comput. Phys. , vol.121 , pp. 51
    • Dai, W.1    Woodward, P.R.2
  • 2
    • 0000128492 scopus 로고
    • A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
    • A. L. Zachary, A. Malagoli, and P. Colella, A higher-order Godunov method for multidimensional ideal magnetohydrodynamics, SIAM J. Sci. Stat. Comp. 15 (1994).
    • (1994) SIAM J. Sci. Stat. Comp. , vol.15
    • Zachary, A.L.1    Malagoli, A.2    Colella, P.3
  • 3
    • 0000493663 scopus 로고    scopus 로고
    • Transport magnetic flux in an arbitrary coordinate ALE code
    • R. E. Peterkin, M. H. Frese, and C. R. Sovinec, Transport magnetic flux in an arbitrary coordinate ALE code, J. Comput. Phys. 140, 148 (1998).
    • (1998) J. Comput. Phys. , vol.140 , pp. 148
    • Peterkin, R.E.1    Frese, M.H.2    Sovinec, C.R.3
  • 5
    • 0031568136 scopus 로고    scopus 로고
    • An implicit scheme for nonideal magnetohydrodynamics
    • O. S. Jones, U. Shumlak, and D. S. Eberhardt, An implicit scheme for nonideal magnetohydrodynamics, J. Comput. Phys. 130, 231 (1997).
    • (1997) J. Comput. Phys. , vol.130 , pp. 231
    • Jones, O.S.1    Shumlak, U.2    Eberhardt, D.S.3
  • 8
    • 84982200411 scopus 로고
    • Towards a numerical error bar in CFD
    • G. E. Karniadakis, Towards a numerical error bar in CFD, J. Fuids Eng. 117, 7 (1995).
    • (1995) J. Fuids Eng. , vol.117 , pp. 7
    • Karniadakis, G.E.1
  • 9
    • 0000236567 scopus 로고
    • Evolution of the Orszag-Tang vortex system in a compressible medium. I. Initial average subsonic flow
    • R. B. Dahlburg and J. M. Picone, Evolution of the Orszag-Tang vortex system in a compressible medium. I. Initial average subsonic flow, Phys. Fluids B 1(11), 2153 (1989).
    • (1989) Phys. Fluids B , vol.1 , Issue.11 , pp. 2153
    • Dahlburg, R.B.1    Picone, J.M.2
  • 10
    • 0001241567 scopus 로고    scopus 로고
    • A stable penalty method for the compressible Navier-Stokes equations. I. Open boundary conditions
    • J. S. Hesthaven and D. Gottlieb, A stable penalty method for the compressible Navier-Stokes equations. I. Open boundary conditions, SIAM J. Sci. Comp. 17(3), 579 (1996).
    • (1996) SIAM J. Sci. Comp. , vol.17 , Issue.3 , pp. 579
    • Hesthaven, J.S.1    Gottlieb, D.2
  • 11
    • 0001257477 scopus 로고
    • Multidomain spectral solutions of compressible viscous flows
    • D. A. Kopriva, Multidomain spectral solutions of compressible viscous flows, J. Comput. Phys. 115, 184 (1994).
    • (1994) J. Comput. Phys. , vol.115 , pp. 184
    • Kopriva, D.A.1
  • 12
    • 0001809357 scopus 로고
    • A spectral element-FCT method for the compressible Euler equations
    • J. Giannakouros and G. E. Karniadakis, A spectral element-FCT method for the compressible Euler equations, J. Comput. Phys. 115, 65 (1994).
    • (1994) J. Comput. Phys. , vol.115 , pp. 65
    • Giannakouros, J.1    Karniadakis, G.E.2
  • 13
    • 0000194504 scopus 로고
    • Simulation of magnetohydrodynamic flows: A constrained transport method
    • C. R. Evans and J. F. Hawley, Simulation of magnetohydrodynamic flows: A constrained transport method, Astro. Phys. J. 332, 659 (1988).
    • (1988) Astro. Phys. J. , vol.332 , pp. 659
    • Evans, C.R.1    Hawley, J.F.2
  • 14
    • 85190165993 scopus 로고    scopus 로고
    • Analysis and numerical approximation of a stationary MHD flow problem with nonideal boundary
    • in press
    • A. J. Meir and P. G. Schmidt, Analysis and numerical approximation of a stationary MHD flow problem with nonideal boundary, SIAM J. Numer. Anal., in press.
    • SIAM J. Numer. Anal.
    • Meir, A.J.1    Schmidt, P.G.2
  • 15
    • 0001234668 scopus 로고    scopus 로고
    • Spectral/hp methods for viscous compressible flows on unstructured 2d meshes
    • I. Lomtev, C. B. Quillen, and G. E. Karniadakis, Spectral/hp methods for viscous compressible flows on unstructured 2d meshes, J. Comput. Phys. 144(2), 325 (1998).
    • (1998) J. Comput. Phys. , vol.144 , Issue.2 , pp. 325
    • Lomtev, I.1    Quillen, C.B.2    Karniadakis, G.E.3
  • 16
    • 0033558751 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for the Navier-Stokes equations
    • I. Lomtev and G. E. Karniadakis, A discontinuous Galerkin method for the Navier-Stokes equations, Int. J. Numer. Methods Fluids 29, 587 (1999).
    • (1999) Int. J. Numer. Methods Fluids , vol.29 , pp. 587
    • Lomtev, I.1    Karniadakis, G.E.2
  • 17
    • 85190119133 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for the Euler and the Navier-Stokes equations
    • in press
    • C. E. Baumann and T. J. Oden, A discontinuous hp finite element method for the Euler and the Navier-Stokes equations, Int. J. Numer. Method Fluids, in press.
    • Int. J. Numer. Method Fluids
    • Baumann, C.E.1    Oden, T.J.2
  • 18
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems
    • J. T. Oden, I. Babuska, and C. E. Baumann, A discontinuous hp finite element method for diffusion problems, J. Comput. Phys. 146, 491 (1998).
    • (1998) J. Comput. Phys. , vol.146 , pp. 491
    • Oden, J.T.1    Babuska, I.2    Baumann, C.E.3
  • 19
    • 85190143064 scopus 로고    scopus 로고
    • Stabilized hp-finite element approximations of hyperbolic problems
    • in press
    • P. Houston, C. Schwab, and E. Suli, Stabilized hp-finite element approximations of hyperbolic problems, SIAM J. Numer. Anal., in press.
    • SIAM J. Numer. Anal.
    • Houston, P.1    Schwab, C.2    Suli, E.3
  • 20
    • 0018286867 scopus 로고
    • Small-scale structure of two-dimensional magnetohydrodynamic turbulence
    • S. A. Orszag and C. Tang, Small-scale structure of two-dimensional magnetohydrodynamic turbulence, J. Fluid Mech. 90(1), 129 (1979).
    • (1979) J. Fluid Mech. , vol.90 , Issue.1 , pp. 129
    • Orszag, S.A.1    Tang, C.2
  • 21
    • 0026371189 scopus 로고
    • Spectral methods on triangles and other domains
    • M. Dubiner, Spectral methods on triangles and other domains, J. Sci. Comput. 6, 345 (1991).
    • (1991) J. Sci. Comput. , vol.6 , pp. 345
    • Dubiner, M.1
  • 22
    • 0029410227 scopus 로고
    • A new triangular and tetrahedral basis for high-order finite element methods
    • S. J. Sherwin and G. E. Karniadakis, A new triangular and tetrahedral basis for high-order finite element methods, Int. J. Numer. Methods Eng. 123, 3775 (1995).
    • (1995) Int. J. Numer. Methods Eng. , vol.123 , pp. 3775
    • Sherwin, S.J.1    Karniadakis, G.E.2
  • 23
    • 0031235643 scopus 로고    scopus 로고
    • Hierarchical hp finite elements in hybrid domains
    • S. J. Sherwin, Hierarchical hp finite elements in hybrid domains, Finite Elem. Anal. Des. 27, 109 (1997).
    • (1997) Finite Elem. Anal. Des. , vol.27 , pp. 109
    • Sherwin, S.J.1
  • 24
    • 0030096938 scopus 로고    scopus 로고
    • Tetrahedral hp finite elements: Algorithms and flow simulations
    • S. J. Sherwin and G. E. Karniadakis, Tetrahedral hp finite elements: Algorithms and flow simulations, J. Comput. Phys. 124, 14 (1996).
    • (1996) J. Comput. Phys. , vol.124 , pp. 14
    • Sherwin, S.J.1    Karniadakis, G.E.2
  • 26
    • 84968487025 scopus 로고
    • On a cell entropy inequality for discontinuous Galerkin methods
    • G. Jiang and C. W. Shu, On a cell entropy inequality for discontinuous Galerkin methods, Math. Comp. 62, 531 (1994).
    • (1994) Math. Comp. , vol.62 , pp. 531
    • Jiang, G.1    Shu, C.W.2
  • 27
    • 85190118561 scopus 로고    scopus 로고
    • The local discontinuous Galerkin for time dependent convection-diffusion systems
    • in press
    • B. Cockburn and C. W. Shu, The local discontinuous Galerkin for time dependent convection-diffusion systems, SIAM J. Numer. Anal., in press.
    • SIAM J. Numer. Anal.
    • Cockburn, B.1    Shu, C.W.2
  • 29
    • 0029277387 scopus 로고
    • Numerical simulation of the MHD equations by a kinetic-type method
    • J. Croisille, R. Khanfir, and G. Chanteur, Numerical simulation of the MHD equations by a kinetic-type method, J. Sci. Comput. 10(1), 81 (1995).
    • (1995) J. Sci. Comput. , vol.10 , Issue.1 , pp. 81
    • Croisille, J.1    Khanfir, R.2    Chanteur, G.3
  • 32
    • 85190101368 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems: ID analysis
    • in press
    • I. Babuska, C. E. Baumann, and T. J. Oden, A discontinuous hp finite element method for diffusion problems: ID analysis, Comput. Math. Appl., in press.
    • Comput. Math. Appl.
    • Babuska, I.1    Baumann, C.E.2    Oden, T.J.3
  • 33
    • 0001689247 scopus 로고
    • The effect of nonzero ∇·B on the numerical solution of the magnetohydrodynamic equations
    • J. U. Brackbill and D. C. Barnes, The effect of nonzero ∇·B on the numerical solution of the magnetohydrodynamic equations, J. Comput. Phys. 35, 426 (1980).
    • (1980) J. Comput. Phys. , vol.35 , pp. 426
    • Brackbill, J.U.1    Barnes, D.C.2
  • 37
    • 85043296875 scopus 로고    scopus 로고
    • Numerical simulation of the two-dimensional MHD flow around a circular cylinder
    • V. Shatrov, G. Mutschke, and G. Gerbeth, Numerical simulation of the two-dimensional MHD flow around a circular cylinder, Magnetohydrodynamics 33, 3 (1997).
    • (1997) Magnetohydrodynamics , vol.33 , pp. 3
    • Shatrov, V.1    Mutschke, G.2    Gerbeth, G.3
  • 38
    • 0031661317 scopus 로고    scopus 로고
    • Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forces localized on the cylinder surface
    • T. Weier, G. Gerbeth, G. Mutschke, E. Platacis, and O. Lielausis, Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forces localized on the cylinder surface, Exp. Therm. Fluid Sci. 16, 84 (1998).
    • (1998) Exp. Therm. Fluid Sci. , vol.16 , pp. 84
    • Weier, T.1    Gerbeth, G.2    Mutschke, G.3    Platacis, E.4    Lielausis, O.5
  • 40
    • 0343980569 scopus 로고
    • Tetrahedral hp finite elements: Algorithms and flow simulations
    • S. J. Sherwin and G. E. Karniadakis, Tetrahedral hp finite elements: Algorithms and flow simulations, J. Comput. Phys. 122, 191 (1995).
    • (1995) J. Comput. Phys. , vol.122 , pp. 191
    • Sherwin, S.J.1    Karniadakis, G.E.2
  • 41
    • 84966236671 scopus 로고
    • Non-oscillatory spectral Fourier methods for shock wave calculations
    • W. Cai, D. Gottlieb, and C. W. Shu, Non-oscillatory spectral Fourier methods for shock wave calculations, Math. Comp. 52, 389 (1989).
    • (1989) Math. Comp. , vol.52 , pp. 389
    • Cai, W.1    Gottlieb, D.2    Shu, C.W.3
  • 42
    • 0038363138 scopus 로고    scopus 로고
    • Spectral approximations on the triangle
    • R. G. Owens, Spectral approximations on the triangle, Proc. R. Soc. London A 454, 857 (1998).
    • (1998) Proc. R. Soc. London A , vol.454 , pp. 857
    • Owens, R.G.1
  • 43
    • 85190109574 scopus 로고    scopus 로고
    • The natural function space for triangular and tetrahedral spectral elements
    • in press
    • B. A. Wingate and M. A. Taylor, The natural function space for triangular and tetrahedral spectral elements, SIAM J. Numer. Anal., in press.
    • SIAM J. Numer. Anal.
    • Wingate, B.A.1    Taylor, M.A.2


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