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
A numerical study of a rotationally degenerate hyperbolic system. Part I: The Riemann problem
Journal of Computational Physics
An approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
A numerical study of a rotationally degenerate hyperbolic system. Part II. The Cauchy problem
SIAM Journal on Numerical Analysis
Notes on the eigensystem of magnetohydrodynamics
SIAM Journal on Applied Mathematics
Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
On Godunov-type schemes for magnetohydrodynamics
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
Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics
Journal of Computational Physics
Compact third-order limiter functions for finite volume methods
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
Detailed empirical error and convergence studies for high order weighted essentially non-oscillatory (WENO) schemes are presented in the case of special magnetohydrodynamic Riemann problems. The results supplement the results for standard high resolution finite volume schemes given in [M. Torrilhon, Non-uniform convergence of finite-volume-schemes for Riemann problems of ideal magnetohydrodynamics, J. Comput. Phys. 192 (2003) 73-94]. The special Riemann problems are based on initial conditions that are close to initial conditions which admit non-unique solutions. Like the standard methods the WENO schemes investigated in this paper exhibit a strongly non-uniform convergence behavior with initial convergence to a wrong solution (pseudo-convergence). However, the cancelation of the pseudo-convergence occurs at coarser grids for higher order methods.