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
Higher order Godunov methods for general systems of hyperbolic conservation laws
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
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
Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics
Journal of Computational Physics
SIAM Journal on Scientific Computing
An Adaptive Mesh Projection Method for Viscous Incompressible Flow
SIAM Journal on Scientific Computing
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 Fast Direct Solver for Elliptic Partial Differential Equations on Adaptively Refined Meshes
SIAM Journal on Scientific Computing
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A cell-centered adaptive projection method for the incompressible Euler equations
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
Approximate Projection Methods: Part I. Inviscid Analysis
SIAM Journal on Scientific Computing
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
Journal of Computational Physics
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
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
A stable and convergent scheme for viscoelastic flow in contraction channels
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 | 31.51 |
We present a second-order Godunov algorithm for multidimensional, ideal MHD. Our algorithm is based on the unsplit formulation of Colella (J. Comput. Phys. 87, 1990), with all of the primary dependent variables centered at the same location. To properly represent the divergence-free condition of the magnetic fields, we apply a discrete projection to the intermediate values of the field at cell faces, and apply a filter to the primary dependent variables at the end of each time step. We test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions. The test suite includes rotated planar linear waves, MHD shock tube problems, low-beta flux tubes, and a magnetized rotor problem. For all of these cases, we observe that the algorithm is second-order accurate for smooth solutions, converges to the correct weak solution for problems involving shocks, and exhibits no evidence of instability or loss of accuracy due to the possible presence of non-solenoidal fields.