메뉴 건너뛰기




Volumn 204, Issue 2, 2005, Pages 737-759

Central finite volume methods with constrained transport divergence treatment for ideal MHD

Author keywords

Central schemes; Magnetohydrodynamics; Non oscillatory; Numerical methods

Indexed keywords

FINITE VOLUME METHOD; MAGNETOHYDRODYNAMICS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 15944380439     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.10.034     Document Type: Article
Times cited : (12)

References (53)
  • 1
    • 0002715573 scopus 로고
    • Généralisation du schéma de Nessayahu-Tadmor pour une équation hyperbolique à deux dimensions d'espace
    • t.320, serie I
    • P. Arminjon, M.C. Viallon, Généralisation du schéma de Nessayahu-Tadmor pour une équation hyperbolique à deux dimensions d'espace, CR Acad. Sci. Paris, t.320, serie I, 1995, pp. 85-88
    • (1995) CR Acad. Sci. Paris , pp. 85-88
    • Arminjon, P.1    Viallon, M.C.2
  • 2
    • 0001884854 scopus 로고
    • A two-dimensional finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flows
    • M. Hafez, K. Oshima, (Eds.)
    • P. Arminjon, D. Stanescu, M.C. Viallon, A two-dimensional finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flows, in: M. Hafez, K. Oshima, (Eds.), Proceedings of the Sixth International Symposium on Computational Fluid Dynamics, vol. IV, 1995, pp. 7-14
    • (1995) Proceedings of the Sixth International Symposium on Computational Fluid Dynamics , vol.4 , pp. 7-14
    • Arminjon, P.1    Stanescu, D.2    Viallon, M.C.3
  • 3
    • 0031325623 scopus 로고    scopus 로고
    • A finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for conservation laws on unstructured grids, revised version with numerical applications
    • P. Arminjon M.C. Viallon A. Madrane A finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for conservation laws on unstructured grids, revised version with numerical applications Int. J. Comput. Fluid Dynamics 9 No. 1 1997 1-22
    • (1997) Int. J. Comput. Fluid Dynamics , vol.9 , Issue.1 , pp. 1-22
    • Arminjon, P.1    Viallon, M.C.2    Madrane, A.3
  • 4
    • 0033343669 scopus 로고    scopus 로고
    • Staggered mixed finite volume/finite element method for Navier-Stokes equations
    • P. Arminjon A. Madrane Staggered mixed finite volume/finite element method for Navier-Stokes equations AIAA J. 37 1999 1558-1571
    • (1999) AIAA J. , vol.37 , pp. 1558-1571
    • Arminjon, P.1    Madrane, A.2
  • 5
    • 0000954323 scopus 로고    scopus 로고
    • Convergence of a finite volume extension of the Nessyahu-Tadmor scheme on unstructured grids for a two-dimensional linear hyperbolic equation
    • P. Arminjon M.C. Viallon Convergence of a finite volume extension of the Nessyahu-Tadmor scheme on unstructured grids for a two-dimensional linear hyperbolic equation SIAM J. Num. Anal. 36 No. 3 1999 738-771
    • (1999) SIAM J. Num. Anal. , vol.36 , Issue.3 , pp. 738-771
    • Arminjon, P.1    Viallon, M.C.2
  • 6
    • 84983135010 scopus 로고    scopus 로고
    • New Lax-Friedrichs-type finite volume schemes on 2 and 3D Cartesian staggered grids
    • J. Militzer, (Ed.) Halifax 1999
    • P. Arminjon, A. Madrane, A. St-Cyr, New Lax-Friedrichs-type finite volume schemes on 2 and 3D Cartesian staggered grids, in: J. Militzer, (Ed.), Seventh Annual Conference of the CFD Society of Canada, 1999, Halifax, 1999, pp. (3-3)-(3-10)
    • (1999) Seventh Annual Conference of the CFD Society of Canada
    • Arminjon, P.1    Madrane, A.2    St-Cyr, A.3
  • 7
    • 0038570151 scopus 로고    scopus 로고
    • Numerical simulation of 3-D flows with a non-oscillatory central scheme on staggered unstructured tetrahedral grids
    • H. Freistuehler, G. Warnecke, Birkhauser, (Eds.) Int. Series of Num. Math. ISBN 3-7643-6711-3
    • P. Arminjon, A. Madrane, A. St-Cyr, Numerical simulation of 3-D flows with a non-oscillatory central scheme on staggered unstructured tetrahedral grids, in: H. Freistuehler, G. Warnecke, Birkhauser, (Eds.), Proceedings of the Eighth International Conference on Hyperbolic Problems, Int. Series of Num. Math. vol. 140, 2001, pp. 59-68, ISBN 3-7643-6711-3
    • (2001) Proceedings of the Eighth International Conference on Hyperbolic Problems , vol.140 , pp. 59-68
    • Arminjon, P.1    Madrane, A.2    St-Cyr, A.3
  • 8
    • 0036467062 scopus 로고    scopus 로고
    • New 2 and 3-dimensional non-oscillatory central finite volume methods for staggered Cartesian grids
    • P. Arminjon A. St-Cyr A. Madrane New 2 and 3-dimensional non-oscillatory central finite volume methods for staggered Cartesian grids Appl. Numer. Math. 40/3 2002 367-390
    • (2002) Appl. Numer. Math. , vol.40 , Issue.3 , pp. 367-390
    • Arminjon, P.1    St-Cyr, A.2    Madrane, A.3
  • 9
    • 0038113066 scopus 로고    scopus 로고
    • Nessyahu-Tadmor-type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids
    • P. Arminjon A. St-Cyr Nessyahu-Tadmor-type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids Appl. Numer. Math. 46 2003 135-155
    • (2003) Appl. Numer. Math. , vol.46 , pp. 135-155
    • Arminjon, P.1    St-Cyr, A.2
  • 10
    • 85190106824 scopus 로고    scopus 로고
    • New three-dimensional structured diamond-staggered finite volume methods
    • December
    • P. Arminjon, R. Touma, New three-dimensional structured diamond-staggered finite volume methods, CRM Res. Rep., December 2003
    • (2003) CRM Res. Rep.
    • Arminjon, P.1    Touma, R.2
  • 12
    • 85190145918 scopus 로고    scopus 로고
    • Central schemes with constrained transport divergence treatment for ideal MHD
    • Proceedings of the 10th International Conference on Hyperbolic Problems, Osaka, September
    • P. Arminjon, R. Touma, Central schemes with constrained transport divergence treatment for ideal MHD, in: Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the 10th International Conference on Hyperbolic Problems, Osaka, September 2004
    • (2004) Hyperbolic Problems: Theory, Numerics, Applications
    • Arminjon, P.1    Touma, R.2
  • 13
    • 0032337254 scopus 로고    scopus 로고
    • Total variation diminishing scheme for adiabatic and isothermal magnetohydrodynamics
    • D.S. Balsara Total variation diminishing scheme for adiabatic and isothermal magnetohydrodynamics Astrophys. J. (Suppl.) 116 1998 133
    • (1998) Astrophys. J. (Suppl.) , vol.116 , pp. 133
    • Balsara, D.S.1
  • 14
    • 0030161576 scopus 로고    scopus 로고
    • Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics
    • A.A. Barmin A.G. Kulikovskiy N.V. Pogorelov Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics J. Comput. Phys. 126 1996 77
    • (1996) J. Comput. Phys. , vol.126 , pp. 77
    • Barmin, A.A.1    Kulikovskiy, A.G.2    Pogorelov, N.V.3
  • 15
    • 0001689247 scopus 로고
    • The effect of nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations
    • J.U. Brackbill D.C. Barnes The effect of nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations J. Comput. Phys. 35 1980 426
    • (1980) J. Comput. Phys. , vol.35 , pp. 426
    • Brackbill, J.U.1    Barnes, D.C.2
  • 16
    • 45449121905 scopus 로고
    • An upwind differencing scheme for the equations of ideal magnetohydrodynamics
    • M. Brio C.C. Wu An upwind differencing scheme for the equations of ideal magnetohydrodynamics J. Comput. Phys. 2 75 1988 400-422
    • (1988) J. Comput. Phys. , vol.2 , Issue.75 , pp. 400-422
    • Brio, M.1    Wu, C.C.2
  • 17
    • 28144445934 scopus 로고
    • An approximate Riemann solver for ideal magnetohydrodynamics
    • W. Dai P.R. Woodward An approximate Riemann solver for ideal magnetohydrodynamics J. Comput. Phys. 111 1994 354-372
    • (1994) J. Comput. Phys. , vol.111 , pp. 354-372
    • Dai, W.1    Woodward, P.R.2
  • 18
    • 0001580138 scopus 로고    scopus 로고
    • A simple finite difference scheme for multidimensional magnetohydro-dynamical equations
    • W. Dai P.R. Woodward A simple finite difference scheme for multidimensional magnetohydro-dynamical equations J. Comput. Phys. 142 1998 331-369
    • (1998) J. Comput. Phys. , vol.142 , pp. 331-369
    • Dai, W.1    Woodward, P.R.2
  • 19
    • 0042487895 scopus 로고
    • Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
    • W. Dai P.R. Woodward Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics J. Comput. Phys. 115 1994 485-513
    • (1994) J. Comput. Phys. , vol.115 , pp. 485-513
    • Dai, W.1    Woodward, P.R.2
  • 20
    • 0003473361 scopus 로고    scopus 로고
    • Numerical simulation and analysis of magnetically dominated MHD bow shock ows with applications in space physics
    • Ph.D. Thesis, Katholieke Unversiteit Leuven
    • A.H. De Sterck, Numerical simulation and analysis of magnetically dominated MHD bow shock ows with applications in space physics, Ph.D. Thesis, Katholieke Unversiteit Leuven, 1999
    • (1999)
    • De Sterck, A.H.1
  • 21
    • 0000194504 scopus 로고
    • Simulation of magnetohydrodynamic flows: A constrained transport method
    • C.R. Evans J.F. Hawley Simulation of magnetohydrodynamic flows: A constrained transport method Astrophys. J. 332 1988 659
    • (1988) Astrophys. J. , vol.332 , pp. 659
    • Evans, C.R.1    Hawley, J.F.2
  • 22
    • 0003828736 scopus 로고    scopus 로고
    • Numerical Approximation of Hyperbolic Systems of Conservations Laws
    • Springer
    • E. Godlewski P.-A. Raviart Numerical Approximation of Hyperbolic Systems of Conservations Laws 1996 Springer
    • (1996)
    • Godlewski, E.1    Raviart, P.-A.2
  • 23
    • 0000935266 scopus 로고
    • A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics
    • S.K. Godunov A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics Math. Sb. 47 89 1959 271-306
    • (1959) Math. Sb. , vol.47 , Issue.89 , pp. 271-306
    • Godunov, S.K.1
  • 24
    • 0004117522 scopus 로고
    • Résolution numérique des problèmes multidimensionnels de la dynamique des gaz, traduit du russe
    • Editions Mir, Moscou
    • S.K. Godunov, A. Zabrodine, M. Ivanov, A. Kraïko, G. Prokopov, Résolution numérique des problèmes multidimensionnels de la dynamique des gaz, traduit du russe Editions Mir, Moscou, 1979
    • (1979)
    • Godunov, S.K.1    Zabrodine, A.2    Ivanov, M.3    Kraïko, A.4    Prokopov, G.5
  • 26
    • 0007513455 scopus 로고    scopus 로고
    • Essential elements of computational algorithms for aerodynamic analysis and design
    • ICASE Report 97-68
    • A. Jameson, Essential elements of computational algorithms for aerodynamic analysis and design, ICASE Report, 97-68, 1997
    • (1997)
    • Jameson, A.1
  • 28
    • 0032206542 scopus 로고    scopus 로고
    • Non-oscillatory central schemes for multidimensional hyperbolic conservation laws
    • G. Jiang E. Tadmor Non-oscillatory central schemes for multidimensional hyperbolic conservation laws SIAM J. Sci. Comput. 19 1998 1892-1917
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1892-1917
    • Jiang, G.1    Tadmor, E.2
  • 29
    • 0001116632 scopus 로고    scopus 로고
    • A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
    • G. Jiang C.C. Wu A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics J. Comput. Phys. 150 1999 561-594
    • (1999) J. Comput. Phys. , vol.150 , pp. 561-594
    • Jiang, G.1    Wu, C.C.2
  • 30
    • 0007741184 scopus 로고    scopus 로고
    • A modified structured central scheme for 2D hyperbolic conservation laws
    • T. Katsaounis D. Levy A modified structured central scheme for 2D hyperbolic conservation laws Appl. Math. Lett. 12 6 1999 86-89
    • (1999) Appl. Math. Lett. , vol.12 , Issue.6 , pp. 86-89
    • Katsaounis, T.1    Levy, D.2
  • 31
    • 0004186233 scopus 로고    scopus 로고
    • Numerical Schemes for Conservation Laws
    • Adv. Numer. Math., Wiley, Stuttgart
    • D. Kröner, Numerical Schemes for Conservation Laws, in Wiley-Teubner Series, Adv. Numer. Math., Wiley, Stuttgart, 1997
    • (1997) Wiley-Teubner Series
    • Kröner, D.1
  • 33
    • 84980078953 scopus 로고
    • Weak solutions of nonlinear hyperbolic equation and their numerical computation
    • P.D. Lax Weak solutions of nonlinear hyperbolic equation and their numerical computation Comm. Pure Appl. Math. 7 1954 159-193
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 159-193
    • Lax, P.D.1
  • 36
    • 0007797061 scopus 로고    scopus 로고
    • Remarks on high-resolution non-oscillatory central schemes for multidimensional systems of conservation laws. Part I: An improved quadrature rule for the flux computation
    • Preprint No. 679, Sonderforschungsbereich 256, Rheinische Friedrich-Wilhelms-Universitaet, Bonn, Germany
    • K.-A. Lie, S. Noelle, Remarks on high-resolution non-oscillatory central schemes for multidimensional systems of conservation laws. Part I: An improved quadrature rule for the flux computation, Preprint No. 679, Sonderforschungsbereich 256, Rheinische Friedrich-Wilhelms-Universitaet, Bonn, Germany, 2000
    • (2000)
    • Lie, K.-A.1    Noelle, S.2
  • 37
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • H. Nessyahu E. Tadmor Non-oscillatory central differencing for hyperbolic conservation laws J. Comput. Phys. 87 2 1990 408-463
    • (1990) J. Comput. Phys. , vol.87 , Issue.2 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 38
    • 85190125292 scopus 로고    scopus 로고
    • Central Runge-Kutta schemes for Conservation Laws
    • Preprint submitted to
    • L. Pareschi, G. Puppo, G. Russo, Central Runge-Kutta schemes for Conservation Laws, Preprint submitted to SIAM J. Sci. Comput., 2003
    • (2003) SIAM J. Sci. Comput.
    • Pareschi, L.1    Puppo, G.2    Russo, G.3
  • 41
    • 0008104353 scopus 로고
    • An Approximate Riemann Solver for MHD
    • ICASE NASA, Langley Research Center, Contract Rep. 194902, ICASE Rep. 94-25, Hampton, VA
    • K.G. Powell, An Approximate Riemann Solver for MHD, ICASE NASA, Langley Research Center, Contract Rep. 194902, ICASE Rep. 94-25, Hampton, VA, 1994
    • (1994)
    • Powell, K.G.1
  • 43
    • 15344342039 scopus 로고    scopus 로고
    • I. Struckmeier, (Eds.) Hyp. Part. Diff. Eq., Theo., Num. App., A. Meister, Vieweg, Wiesbaden (D)
    • G. Russo, in: I. Struckmeier, (Eds.), Central schemes and Systems of Balance Laws, Hyp. Part. Diff. Eq., Theo., Num. App., A. Meister, Vieweg, Wiesbaden (D), 2002
    • (2002) Central Schemes and Systems of Balance Laws
    • Russo, G.1
  • 44
    • 11944265404 scopus 로고
    • Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for one-dimensional flow
    • D. Ryu T.W. Jones Numerical magnetohydrodynamics in astrophysics: algorithm and tests for one-dimensional flow Astrophys. J. 442 1995 228
    • (1995) Astrophys. J. , vol.442 , pp. 228
    • Ryu, D.1    Jones, T.W.2
  • 45
    • 0003332686 scopus 로고
    • Numerical solution of the Riemann problem for two-dimensional gas dynamics
    • C.W. Schulz-Rinne J.P. Collins H.M. Glaz Numerical solution of the Riemann problem for two-dimensional gas dynamics SIAM J. Sci. Comput. 14 1993 1394-1414
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1394-1414
    • Schulz-Rinne, C.W.1    Collins, J.P.2    Glaz, H.M.3
  • 48
    • 0346046827 scopus 로고    scopus 로고
    • The ∇ · B=0 constraint in shock-capturing magnetohydrodynamics codes
    • G. Tóth The ∇ · B = 0 constraint in shock-capturing magnetohydrodynamics codes J. Comput. Phys. 161 2000 605-652
    • (2000) J. Comput. Phys. , vol.161 , pp. 605-652
    • Tóth, G.1
  • 49
    • 0030268703 scopus 로고    scopus 로고
    • Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems
    • G. Tóth D. Odstrčil Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems J. Comput. Phys. 128 1996 82
    • (1996) J. Comput. Phys. , vol.128 , pp. 82
    • Tóth, G.1    Odstrčil, D.2
  • 50
    • 49449129017 scopus 로고
    • Towards the ultimate conservative difference scheme IV. A new approach to numerical convection
    • B. van Leer Towards the ultimate conservative difference scheme IV. A new approach to numerical convection J. Comput. Phys. 23 1977 276-299
    • (1977) J. Comput. Phys. , vol.23 , pp. 276-299
    • van Leer, B.1
  • 51
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
    • B. van Leer Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method J. Comput. Phys. 32 1979 101-136
    • (1979) J. Comput. Phys. , vol.32 , pp. 101-136
    • van Leer, B.1
  • 52
    • 0000008663 scopus 로고
    • A high-order Godunov method for the equations of ideal magnetohydrodynamics
    • A.L. Zachary P. Colella A high-order Godunov method for the equations of ideal magnetohydrodynamics J. Comput. Phys. 99 1992 341-347
    • (1992) J. Comput. Phys. , vol.99 , pp. 341-347
    • Zachary, A.L.1    Colella, P.2
  • 53
    • 0000128492 scopus 로고
    • A higher-order Godunov method for multi-dimensional ideal magnetohydrodynamics
    • A.L. Zachary A. Malagoli P. Colella A higher-order Godunov method for multi-dimensional ideal magnetohydrodynamics SIAM J. Sci. Comput. 15 1994 263-284
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 263-284
    • Zachary, A.L.1    Malagoli, A.2    Colella, P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.