An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
A third order central WENO scheme for 2D conservation laws
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
Divergence- and curl-preserving prolongation and restriction formulas
Journal of Computational Physics
Journal of Computational Physics
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
Journal of Computational Physics
A central-constrained transport scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
SIAM Journal on Scientific Computing
An Unstaggered, High-Resolution Constrained Transport Method for Magnetohydrodynamic Flows
SIAM Journal on Scientific Computing
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
A fourth-order divergence-free method for MHD flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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This paper extends the central finite-volume schemes of Liu et al. [Y. Liu, C.-W. Shu, E. Tadmor, M. Zhang, Non-oscillatory hierarchical reconstruction for central and finite-volume schemes, Commun. Comput. Phys. 2 (2007) 933-963] on overlapping cells to the magneto-hydrodynamic (MHD) equations. In particular, we propose a high order divergence-free reconstruction for the magnetic field that uses the face-centered values. We also advance the magnetic field with a high order constrained transport (CT) scheme to preserve the divergence-free condition to machine round-off error. The overlapping cells are natural to be used to calculate the electric field flux without an averaging procedure. We have developed a third-order scheme which is verified by the numerical experiments. Other higher order schemes can be constructed accordingly. Our central constrained transport schemes do not need characteristic decomposition, and are easy to code and combine with un-split discretization of the source and parabolic terms. The overlapping cell representation of the solution is also used to develop more compact reconstruction and less dissipative schemes. The high resolution is achieved by non-oscillatory hierarchical reconstruction, which does not require characteristic decomposition either. The numerical comparisons show that the central schemes with non-CT perform as well as with CT for most of problems. Numerical examples are given to demonstrate efficacy of the new schemes.