A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
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)
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
Journal of Scientific Computing
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme
Journal of Computational Physics
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This paper extends our previous third-order method [S. Li, High order central scheme on overlapping cells for magneto-hydrodynamic flows with and without constrained transport method, J. Comput. Phys. 227 (2008) 7368-7393] to the fourth-order. Central finite-volume schemes on overlapping grid are used for both the volume-averaged variables and the face-averaged magnetic field. The magnetic field at the cell boundaries falls within the dual grid and is naturally continuous so that our method eliminates the instability triggered by the discontinuity in the normal component of the magnetic field. Our fourth-order scheme has much smaller numerical dissipation than the third-order scheme. The divergence-free condition of the magnetic field is preserved by our fourth-order divergence-free reconstruction and the constrained transport method. Numerical examples show that the divergence-free condition is essential to the accuracy of the method when a limiter is used in the reconstruction. The high-order, low-dissipation, and divergence-free properties of this method make it an ideal tool for direct magneto-hydrodynamic turbulence simulations.