An upwind differencing scheme for the equations of ideal magnetohydrodynamics
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
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
An unsplit 3D upwind method for hyperbolic conservation laws
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
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
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 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
An unsplit Godunov method for ideal MHD via constrained transport in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation
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 Computational Physics
A Semidiscrete Finite Volume Constrained Transport Method on Orthogonal Curvilinear Grids
SIAM Journal on Scientific Computing
Journal of Computational Physics
A simple GPU-accelerated two-dimensional MUSCL-Hancock solver for ideal magnetohydrodynamics
Journal of Computational Physics
Hi-index | 31.49 |
We introduce an unsplit staggered mesh scheme (USM) for multidimensional magnetohydrodynamics (MHD) that uses a constrained transport (CT) method with high-order Godunov fluxes and incorporates a new data reconstruction-evolution algorithm for second-order MHD interface states. In this new algorithm, the USM scheme includes so-called ''multidimensional MHD terms'', proportional to @?.B, in a dimensionally-unsplit way in a single update. This data reconstruction-evolution step, extended from the corner transport upwind (CTU) approach of Colella, maintains in-plane dynamics very well, as shown by the advection of a very weak magnetic field loop in 2D. This data reconstruction-evolution algorithm is also of advantage in its consistency and simplicity when extended to 3D. The scheme maintains the @?.B=0 constraint by solving a set of discrete induction equations using the standard CT approach, where the accuracy of the computed electric field directly influences the quality of the magnetic field solution. We address the lack of proper dissipative behavior in the simple electric field averaging scheme and present a new modified electric field construction (MEC) that includes multidimensional derivative information and enhances solution accuracy. A series of comparison studies demonstrates the excellent performance of the full USM-MEC scheme for many stringent multidimensional MHD test problems chosen from the literature. The scheme is implemented and currently freely available in the University of Chicago ASC FLASH Center's FLASH3 release.