Preprint 2005-046

Non-Oscillatory Central Schemes for One- and Two-Dimensional MHD Equations. II High-Order Semi-Discrete Schemes

Jorge Balbas and Eitan Tadmor

Abstract: We present a new family of high-resolution, non-oscillatory semi-discrete central schemes for the approximate solution of the ideal Magnetohydrodynamics (MHD) equations. This is the second part of our work, where we are passing from the fully-discrete staggered schemes in {BTW}[J. Balb{\'a}s, E. Tadmor, and C.-C. Wu, Non-oscillatory central schemes for one- and two-dimensional {MHD} equations. {I}. JCP, 201(1):261--285, 2004]. to the semi-discrete formulation advocated in [A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. JCP, 160(1):241--282, 2000]. This semi-discrete formulation retains the simplicity of fully-discrete central schemes while enhancing efficiency and adding versatility. The semi-discrete algorithm offers a wider range of options to implement its two key steps: non-oscillatory reconstruction of point values followed by the evolution of the corresponding point valued fluxes. We present the solution of several prototype MHD problems. Solutions of one-dimensional Brio-Wu shock-tube problems and the two-dimensional Kelvin-Helmholtz instability, Orszag-Tang vortex system, and the disruption of a high density cloud by a strong shock are carried out using third- and fourth-order central schemes based on the CWENO reconstructions. These results complement those presented in \cite{BTW} and confirm the remarkable versatility and simplicity of central schemes as black-box, Jacobian-free MHD solvers. Furthermore, our numerical experiments demonstrate that this family of semi-discrete central schemes preserves the $\nabla \cdot {\mathbf B} = 0$-constraint within machine round-off error; happily, no constrained-transport enforcement is needed.

Available as PDF (5.1 Mbytes).
Jorge Balbas, email: jbalbas at umich dot edu
Eitan Tadmor, email: tadmor at cscamm dot umd dot edu
Publishing information:
SIAM Journal on Scientific Computing
Submitted by:
tadmor at cscamm dot umd dot edu November 3 2005.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Mon Nov 7 13:38:42 MET 2005