An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
Journal of Computational Physics
A higher-order Godunov method for multidimensional ideal magnetohydrodynamics
SIAM Journal on Scientific Computing
An approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Notes on the eigensystem of magnetohydrodynamics
SIAM Journal on Applied Mathematics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Maintaining pressure positivity in magnetohydrodynamic simulations
Journal of Computational Physics
A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
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
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
A Semidiscrete Finite Volume Constrained Transport Method on Orthogonal Curvilinear Grids
SIAM Journal on Scientific Computing
Journal of Computational Physics
Positivity-preserving DG and central DG methods for ideal MHD equations
Journal of Computational Physics
High-order central ENO finite-volume scheme for ideal MHD
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.50 |
In a pair of earlier papers the author showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes for MHD. Second order accurate divergence-free schemes for MHD have shown themselves to be very useful in several areas of science and engineering. However, certain computational MHD problems would be much benefited if the schemes had third and higher orders of accuracy. In this paper we show that the reconstruction of divergence-free vector fields can be carried out with better than second order accuracy. As a result, we design divergence-free weighted essentially non-oscillatory (WENO) schemes for MHD that have order of accuracy better than second. A multi-stage Runge-Kutta time integration is used to ensure that the temporal accuracy matches the spatial accuracy. While this is achieved quite simply up to third order in time, going beyond third order is most simply achieved by using the ADER-WENO schemes that are detailed in a companion paper. (ADER stands for Arbitrary Derivative Riemann Problem.) Accuracy analysis is carried out and it is shown that the schemes meet their design accuracy for smooth problems. Stringent tests are also presented showing that the schemes perform well on those tests.