A method for incorporating Gauss' lasw into electromagnetic pic codes
Journal of Computational Physics
An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
Journal of Computational Physics
A higher-order Godunov method for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
On a finite-element method for solving the three-dimensional Maxwell equations
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
A simple Riemann solver and high-order Godunov schemes for hyperbolic systems of conservation laws
Journal of Computational Physics
Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics
Journal of Computational Physics
The origin of spurious solutions in computational electromagnetics
Journal of Computational Physics
Developing numerical fluxes with new sonic fix for MHD equations
Journal of Computational Physics
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Journal of Computational Physics
An entropic solver for ideal lagrangian magnetohydrodynamics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Divergence correction techniques for Maxwell solvers based on a hyperbolic model
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
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)
Divergence- and curl-preserving prolongation and restriction formulas
Journal of Computational Physics
Journal of Computational Physics
A central-constrained transport scheme for ideal magnetohydrodynamics
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
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Locally divergence-free discontinuous Galerkin methods for MHD equations
Journal of Scientific Computing
A level set approach to simulate magnetohydrodynamic-instabilities in aluminum reduction cells
Journal of Computational Physics
A parallel explicit/implicit time stepping scheme on block-adaptive grids
Journal of Computational Physics
Journal of Computational Physics
Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
Journal of Computational Physics
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
Journal of Computational Physics
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations
Applied Numerical Mathematics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Journal of Computational Physics
An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations
Journal of Computational Physics
Journal of Computational Physics
Adaptive numerical algorithms in space weather modeling
Journal of Computational Physics
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
Journal of Computational Physics
Smoothed particle hydrodynamics and magnetohydrodynamics
Journal of Computational Physics
Particle simulations of space weather
Journal of Computational Physics
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
Journal of Computational Physics
Journal of Computational Physics
A simple GPU-accelerated two-dimensional MUSCL-Hancock solver for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.64 |
In simulations of magnetohydrodynamic (MHD) processes the violation of the divergence constraint causes severe stability problems. In this paper we develop and test a new approach to the stabilization of numerical schemes. Our technique can be easily implemented in any existing code since there is no need to modify the solver for the MHD equations. It is based on a modified system in which the divergence constraint is coupled with the conservation laws by introducing a generalized Lagrange multiplier. We suggest a formulation in which the divergence errors are transported to the domain boundaries with the maximal admissible speed and are damped at the same time. This corrected system is hyperbolic and the density, momentum, magnetic induction, and total energy density are still conserved. In comparison to results obtained without correction or with the standard "divergence source terms," our approach seems to yield more robust schemes with significantly smaller divergence errors.