Free Access
Issue |
ESAIM: M2AN
Volume 43, Number 5, September-October 2009
|
|
---|---|---|
Page(s) | 825 - 852 | |
DOI | https://doi.org/10.1051/m2an/2009006 | |
Published online | 08 April 2009 |
- D.S. Balsara and D. Spicer, A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations. J. Comp. Phys. 149 (1999) 270–292. [Google Scholar]
- T.J. Barth, Numerical methods for gas dynamics systems, in An introduction to recent developments in theory and numerics for conservation laws, D. Kröner, M. Ohlberger and C. Rohde Eds., Springer (1999). [Google Scholar]
- S. Benzoni-Gavage and D. Serre, Multidimensional hyperbolic, Partial differential equations – First-order systems and applications, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford (2007). [Google Scholar]
- N. Besse and D. Kröner, Convergence of the locally divergence free discontinuous Galerkin methods for induction equations for the 2D-MHD system. ESAIM: M2AN 39 (2005) 1177–1202. [Google Scholar]
- J.U. Brackbill and D.C. Barnes, The effect of nonzero divB on the numerical solution of the magnetohydrodynamic equations. J. Comp. Phys. 35 (1980) 426–430. [Google Scholar]
- W. Dai and P.R. Woodward, A simple finite difference scheme for multi-dimensional magnetohydrodynamic equations. J. Comp. Phys. 142 (1998) 331–369. [Google Scholar]
- C. Evans and J.F. Hawley, Simulation of magnetohydrodynamic flow: a constrained transport method. Astrophys. J. 332 (1998) 659. [Google Scholar]
- F.G. Fuchs, S. Mishra and N.H. Risebro, Splitting based finite volume schemes for ideal MHD equations. J. Comp. Phys. 228 (2009) 641–660. [Google Scholar]
- S.K. Godunov, The symmetric form of magnetohydrodynamics equation. Num. Meth. Mech. Cont. Media 1 (1972) 26–34. [Google Scholar]
- J.D. Jackson, Classical Electrodynamics. Third Edn., Wiley (1999). [Google Scholar]
- V. Jovanovič and C. Rohde, Finite volume schemes for Friedrichs systems in multiple space dimensions: a priori and a posteriori error estimates. Num. Meth. PDE 21 (2005) 104–131. [Google Scholar]
- R.J. LeVeque, Finite volume methods for hyperbolic problems. Cambridge University Press (2002). [Google Scholar]
- G.K. Parks, Physics of Space Plasmas: An Introduction. Addition-Wesley (1991). [Google Scholar]
- K.G. Powell, A approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension). Technical report 94-24, ICASE, Langley, VA, USA (1994). [Google Scholar]
- K.G. Powell, P.L. Roe, T.J. Linde, T.I. Gombosi and D.L. De Zeeuw, A solution adaptive upwind scheme for ideal MHD. J. Comp. Phys. 154 (1999) 284–309. [NASA ADS] [CrossRef] [Google Scholar]
- J. Rossmanith, A wave propagation method with constrained transport for shallow water and ideal magnetohydrodynamics. Ph.D. Thesis, University of Washington, Seattle, USA (2002). [Google Scholar]
- D.S. Ryu, F. Miniati, T.W. Jones and A. Frank, A divergence free upwind code for multidimensional magnetohydrodynamic flows. Astrophys. J. 509 (1998) 244–255. [Google Scholar]
- M. Torrilhon, Locally divergence preserving upwind finite volume schemes for magnetohyrodynamic equations. SIAM. J. Sci. Comp. 26 (2005) 1166–1191. [Google Scholar]
- M. Torrilhon and M. Fey, Constraint-preserving upwind methods for multidimensional advection equations. SIAM. J. Num. Anal. 42 (2004) 1694–1728. [Google Scholar]
- G. Toth, The divB = 0 constraint in shock capturing magnetohydrodynamics codes. J. Comp. Phys. 161 (2000) 605–652. [CrossRef] [Google Scholar]
- J-P. Vila and P. Villedeau, Convergence of explicit finite volume scheme for first order symmetric systems. Numer. Math. 94 (2003) 573–602. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.