Free Access
Issue
ESAIM: M2AN
Volume 46, Number 3, May-June 2012
Special volume in honor of Professor David Gottlieb
Page(s) 661 - 680
DOI https://doi.org/10.1051/m2an/2011059
Published online 11 January 2012
  1. R. Artebrant and M. Torrilhon, Increasing the accuracy of local divergence preserving schemes for MHD. J. Comput. Phys. 227 (2008) 3405–3427. [CrossRef] [Google Scholar]
  2. J. Bálbas and E. Tadmor, Non-oscillatory central schemes for one and two-dimensional magnetohydrodynamics II : High-order semi-discrete schemes. SIAM. J. Sci. Comput. 28 (2006) 533–560. [CrossRef] [Google Scholar]
  3. J. Bálbas, E. Tadmor and C.C. Wu, Non-oscillatory central schemes for one and two-dimensional magnetohydrodynamics I. J. Comput. Phys. 201 (2004) 261–285. [CrossRef] [Google Scholar]
  4. D.S. Balsara, Divergence free adaptive mesh refinement for magnetohydrodynamics. J. Comput. Phys. 174 (2001) 614–648. [NASA ADS] [CrossRef] [Google Scholar]
  5. D.S. Balsara and D. Spicer, A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations. J. Comput. Phys. 149 (1999) 270–292. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  6. J.B. Bell, P. Colella and H.M. Glaz, A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257–283. [CrossRef] [Google Scholar]
  7. F. Bouchut, C. Klingenberg and K. Waagan, A multi-wave HLL approximate Riemann solver for ideal MHD based on relaxation I- theoretical framework. Numer. Math. 108 (2007) 7–42. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.U. Brackbill and D.C. Barnes, The effect of nonzero DivB on the numerical solution of the magnetohydrodynamic equations. J. Comput. Phys. 35 (1980) 426–430. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Brio and C.C. Wu, An upwind differencing scheme for the equations of ideal MHD. J. Comput. Phys. 75 (1988) 400–422. [NASA ADS] [CrossRef] [Google Scholar]
  10. A.J. Chorin, Numerical solutions of the Navier-Stokes equations. Math. Comput. 22 (1968) 745–762. [CrossRef] [MathSciNet] [Google Scholar]
  11. W. Dai and P.R. Woodward, A simple finite difference scheme for multi-dimensional magnetohydrodynamic equations. J. Comput. Phys. 142 (1998) 331–369. [NASA ADS] [CrossRef] [Google Scholar]
  12. H. Deconnik, P.L. Roe and R. Struijs, A multi-dimensional generalization of Roe’s flux difference splitter for Euler equations. Comput. Fluids 22 (1993) 215. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Dedner, F. Kemm, D. Kröner, C.D. Munz, T. Schnitzer and M. Wesenberg, Hyperbolic divergence cleaning for the MHD equations. J. Comput. Phys. 175 (2002) 645–673. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  14. C. Evans and J.F. Hawley, Simulation of magnetohydrodynamic flow : a constrained transport method. Astrophys. J. 332 (1998) 659. [NASA ADS] [CrossRef] [Google Scholar]
  15. M. Fey, Multi-dimensional upwingding. (I) The method of transport for solving the Euler equations. J. Comput. Phys. 143 (1998) 159–180. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Fey, Multi-dimensional upwingding.(II) Decomposition of Euler equations into advection equations. J. Comput. Phys. 143 (1998) 181–199. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. Fuchs, S. Mishra and N.H. Risebro, Splitting based finite volume schemes for ideal MHD equations. J. Comput. Phys. 228 (2009) 641–660. [CrossRef] [Google Scholar]
  18. F. Fuchs, A. McMurry, S. Mishra, N.H. Risebro and K. Waagan, Finite volume methods for wave propagation in stratified magneto-atmospheres. Commun. Comput. Phys. 7 (2010) 473–509. [Google Scholar]
  19. F. Fuchs, A.D. McMurry, S. Mishra, N.H. Risebro and K. Waagan, Approximate Riemann solver and robust high-order finite volume schemes for the MHD equations in multi-dimensions. Commun. Comput. Phys. 9 (2011) 324–362. [Google Scholar]
  20. S. Gottlieb, C.W. Shu and E. Tadmor, High order time discretizations with strong stability property. SIAM. Rev. 43 (2001) 89–112. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  21. K.F. Gurski, An HLLC-type approximate Riemann solver for ideal Magneto-hydro dynamics. SIAM. J. Sci. Comput. 25 (2004) 2165–2187. [CrossRef] [Google Scholar]
  22. A. Harten, B. Engquist, S. Osher and S.R. Chakravarty, Uniformly high order accurate essentially non-oscillatory schemes. J. Comput. Phys. 71 (1987) 231–303. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Kurganov and E. Tadmor, New high resolution central schemes for non-linear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 (2000) 241–282. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  24. R.J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems, J. Comput. Phys. 131 (1997) 327–353. [NASA ADS] [CrossRef] [Google Scholar]
  25. R.J. LeVeque, Finite volume methods for hyperbolic problems. Cambridge university press, Cambridge (2002). [Google Scholar]
  26. T.J. Linde, A three adaptive multi fluid MHD model for the heliosphere. Ph.D. thesis, University of Michigan, Ann-Arbor (1998). [Google Scholar]
  27. M. Lukacova-Medvidova, K.W. Morton and G. Warnecke, Evolution Galerkin methods for Hyperbolic systems in two space dimensions. Math. Comput. 69 (2000) 1355–1384. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Lukacova-Medvidova, J. Saibertova and G. Warnecke, Finite volume evolution Galerkin methods for Non-linear hyperbolic systems. J. Comput. Phys. 183 (2003) 533–562. [CrossRef] [Google Scholar]
  29. S. Mishra and E. Tadmor, Constraint preserving schemes using potential-based fluxes. I. Multi-dimensional transport equations. Commun. Comput. Phys. 9 (2010) 688–710. [Google Scholar]
  30. S. Mishra and E. Tadmor, Constraint preserving schemes using potential-based fluxes. II. Genuinely multi-dimensional systems of conservation laws. SIAM J. Numer. Anal. 49 (2011) 1023–1045. [CrossRef] [MathSciNet] [Google Scholar]
  31. A. Mignone et al., Pluto : A numerical code for computational astrophysics. Astrophys. J. Suppl. 170 (2007) 228–242. [NASA ADS] [CrossRef] [Google Scholar]
  32. T. Miyoshi and K. Kusano, A multi-state HLL approximate Riemann solver for ideal magneto hydro dynamics. J. Comput. Phys. 208 (2005) 315–344. [NASA ADS] [CrossRef] [Google Scholar]
  33. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  34. S. Noelle, The MOT-ICE : A new high-resolution wave propagation algorithm for multi-dimensional systems of conservation laws based on Fey’s method of transport. J. Comput. Phys. 164 (2000) 283–334. [CrossRef] [MathSciNet] [Google Scholar]
  35. K.G. Powell, An approximate Riemann solver for magneto-hydro dynamics (that works in more than one space dimension). Technical report, ICASE, Langley, VA (1994) 94–24. [Google Scholar]
  36. 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. Comput. Phys. 154 (1999) 284–309. [NASA ADS] [CrossRef] [Google Scholar]
  37. P.L. Roe and D.S. Balsara, Notes on the eigensystem of magnetohydrodynamics. SIAM. J. Appl. Math. 56 (1996) 57–67. [CrossRef] [Google Scholar]
  38. J. Rossmanith, A wave propagation method with constrained transport for shallow water and ideal magnetohydrodynamics. Ph.D. thesis, University of Washington, Seattle (2002). [Google Scholar]
  39. 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. [NASA ADS] [CrossRef] [Google Scholar]
  40. C.W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory schemes – II. J. Comput. Phys. 83 (1989) 32–78. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  41. E. Tadmor, Approximate solutions of nonlinear conservation laws, in Advanced Numerical approximations of Nonlinear Hyperbolic equations, edited by A. Quarteroni. Lecture notes in Mathematics, Springer Verlag (1998) 1–149. [Google Scholar]
  42. M. Torrilhon, Locally divergence preserving upwind finite volume schemes for magnetohyrodynamic equations. SIAM. J. Sci. Comput. 26 (2005) 1166–1191. [CrossRef] [Google Scholar]
  43. M. Torrilhon and M. Fey, Constraint-preserving upwind methods for multidimensional advection equations. SIAM. J. Numer. Anal. 42 (2004) 1694–1728. [CrossRef] [MathSciNet] [Google Scholar]
  44. G. Toth, The DivB = 0 constraint in shock capturing magnetohydrodynamics codes. J. Comput. Phys. 161 (2000) 605–652. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  45. 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. [NASA ADS] [CrossRef] [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.

Recommended for you