An unsplit Godunov method for ideal MHD via constrained transport in three dimensions

Journal of Computational Physics

Volumn 227, Issue 8, 2008, Pages 4123-4141

  Gardiner, Thomas A ^a   Stone, James M ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Compressible flow; Magnetohydrodynamics; Numerical methods

Indexed keywords

INTERFACE STATES; MAGNETOHYDRODYNAMICS;

CONSTRAINED TRANSPORTS; DIVERGENCE FREE; GODUNOV METHOD; GODUNOV SCHEME; MAGNETIC-FIELD; MULTIDIMENSIONAL INTEGRATION; SECOND ORDERS; SINGLE-STEP; THREE DIMENSIONS; TRANSPORT ALGORITHMS;

NUMERICAL METHODS;

EID: 40249109778     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.12.017     Document Type: Article

References (20)

1. T.A. Gardiner J.M. Stone An unsplit Godunov method for ideal MHD via constrained transport J. Comput. Phys. 205 2005 509
2. S.A. Balbus J.F. Hawley Instability, turbulence, and enhanced transport in accretion disks Rev. Mod. Phys. 70 1998 1
3. D.S. Balsara D.S. Spicer A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations J. Comput. Phys. 149 1999 270
4. A. Brandenburg W.H. Matthaeus Magnetic helicity evolution in a periodic domain with imposed field Phys. Rev. E 69 2004 056407
5. M.A. Berger Magnetic helicity in a periodic domain J. Geophys. Res. 102 1997 2637
6. The effect of nonzero ∇·B on the numerical solution of the magnetohydrodynamic equations
7. P. Colella Multidimensional upwind methods for hyperbolic conservation laws J. Comput. Phys. 87 1990 171
8. P. Colella P.R. Woodward The piecewise parabolic method (PPM) for gas-dynamical simulations J. Comput. Phys. 54 1984 174
9. R.K. Crockett P. Colella R.T. Fisher R.I. Klein C.F. McKee An unsplit, cell-centered Godunov method for ideal MHD J. Comput. Phys. 203 2005 422
10. L. Del Zanna M. Velli P. Londrillo Parametric decay of circularly polarized Alfvén waves: multidimensional simulations in periodic and open domains Astron. Astrophys. 367 2001 705
11. C.R. Evans J.F. Hawley Simulation of magnetohydrodynamic flows: a constrained transport method Astrophys. J. 322 1988 659
12. M.L. Goldstein An instability of finite amplitude circularly polarized Alfvén waves Astrophys. J. 219 1978 700
13. P. Londrillo L. Del Zanna High-order upwind schemes for multidimensional magnetohydrodynamics Astrophys. J. 530 2000 508
14. G.H. Miller P. Colella A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing J. Comput. Phys. 183 2002 26
15. U. Pen P. Arras S. Wong A free, fast, simple and efficient TVD MHD code Astrophys. J. Suppl. 149 2003 447
16. D. Ryu T.W. Jones Numerical magnetohydrodynamics in astrophysics: algorithm and tests for one-dimensional flow Astrophys. J. 442 1995 228
17. J. Saltzman An unsplit 3D upwind method for hyperbolic conservation laws J. Comput. Phys. 115 1994 153
18. J.M. Stone T.A. Gardiner Nonlinear evolution of the magnetohydrodynamic Rayleigh–Taylor instability Phys. Fluids 19 2007 094104
19. The ∇·B=0 constraint in shock-capturing magnetohydrodynamics codes
20. A.L. Zachary A. Malagoli P. Colella A higher-order Godunov method for multidimensional ideal magnetohydrodynamics SIAM J. Sci. Comput. 15 1994 263