Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
Semirelativistic magnetohydrodynamics and physics-based convergence acceleration
Journal of Computational Physics
Solution-Adaptive Magnetohydrodynamics for Space Plasmas: Sun-to-Earth Simulations
Computing in Science and Engineering
A visual fluctuation splitting scheme for magnetohydrodynamics with a new sonic fix and Euler limit
Journal of Computational Physics
A novel approach of divergence-free reconstruction for adaptive mesh refinement
Journal of Computational Physics
Locally divergence-free discontinuous Galerkin methods for MHD equations
Journal of Scientific Computing
A parallel explicit/implicit time stepping scheme on block-adaptive grids
Journal of Computational Physics
An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
Journal of Computational Physics
Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
Journal of Computational Physics
Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD
Journal of Computational Physics
Journal of Computational Physics
Splitting based finite volume schemes for ideal MHD equations
Journal of Computational Physics
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A fourth-order divergence-free method for MHD flows
Journal of Computational Physics
Journal of Computational Physics
An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations
Journal of Computational Physics
Simulations of stellar convection with CO5BOLD
Journal of Computational Physics
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Constrained hyperbolic divergence cleaning for smoothed particle magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
High-order central ENO finite-volume scheme for ideal MHD
Journal of Computational Physics
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An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multi-dimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.