Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Simplified discretization of systems of hyperbolic conservation laws containing advection equations
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
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)
Constraint-Preserving Upwind Methods for Multidimensional Advection Equations
SIAM Journal on Numerical Analysis
Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations
SIAM Journal on Scientific Computing
Limiter-Free Third Order Logarithmic Reconstruction
SIAM Journal on Scientific Computing
Third Order Accurate Non-Polynomial Reconstruction on Rectangular and Triangular Meshes
Journal of Scientific Computing
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Hi-index | 31.45 |
It is of utmost interest to control the divergence of the magnetic flux in simulations of the ideal magnetohydrodynamic equations since, in general, divergence errors tend to accumulate and render the schemes unstable. This paper presents a higher-order extension of the locally divergence-preserving procedure developed in Torrilhon [M. Torrilhon, Locally divergence-preserving upwind finite volume schemes for magnetohydrodynamic equations, SIAM J. Sci. Comput. 26 (2005) 1166-1191]; a fourth-order accurate local redistribution of the numerical magnetic field fluxes of a finite volume base scheme is introduced. The redistribution ensures that a fourth-order accurate discrete divergence operator is preserved to round off errors when applied to the cell averages of the magnetic flux density. The developed procedure is applicable to generic semi-discrete finite volume schemes and its purpose is to stabilize the schemes using a local procedure that respects the accuracy of the base scheme to a greater extent than the previous second-order achievements. Numerical experiments that demonstrate the properties of the new procedure are also presented.