An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
Journal of Computational Physics
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
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
A positive conservative method for magnetohydrodynamics based on HLL and Roe methods
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
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
Divergence- and curl-preserving prolongation and restriction formulas
Journal of Computational Physics
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)
Journal of Computational Physics
An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
Journal of Computational Physics
Hi-index | 31.46 |
A simple novel approach to maintain the divergence-free condition with adaptive mesh refinement is presented. This new approach uses reconstructions on the coarse faces together with the divergence-free condition to reconstruct the field values on the internal fine faces. It does not construct a global interpolation polynomial over a whole coarse cell. Therefore, it can be easily applied to any refinement ratio. It is implemented via a directionally splitting approach so that it can be applied to any kind of grids and in any dimensions. Implementation is presented in the Cartesian, cylindrical and spherical geometries. It is shown by several 2D magneto-hydrodynamic simulations that such a method can keep the divergence-free error of magnetic fields at the round-off level.