On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
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 unsplit 3D upwind method for hyperbolic conservation laws
Journal of Computational Physics
A High-Order Godunov-Type Scheme for Shock Interactions in Ideal Magnetohydrodynamics
SIAM Journal on Scientific Computing
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
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A wave propagation method for three-dimensional hyperbolic conservation laws
Journal of Computational Physics
Hyperbolic divergence cleaning for the MHD equations
Journal of Computational Physics
A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing
Journal of Computational Physics
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
SIAM Journal on Scientific Computing
An HLLC Riemann solver for magneto-hydrodynamics
Journal of Computational Physics
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive 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
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
Journal of Computational Physics
Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation
Journal of Computational Physics
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
A fourth-order divergence-free method for MHD flows
Journal of Computational Physics
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations
Journal of Computational Physics
Journal of Computational Physics
Smoothed particle hydrodynamics and magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A Semidiscrete Finite Volume Constrained Transport Method on Orthogonal Curvilinear Grids
SIAM Journal on Scientific Computing
Journal of Computational Physics
Multi-GPU simulations of Vlasov's equation using Vlasiator
Parallel Computing
Journal of Computational Physics
Pegasus: A new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics
Journal of Computational Physics
Hi-index | 31.54 |
We describe a single step, second-order accurate Godunov scheme for ideal MHD based on combining the piecewise parabolic method (PPM) for performing spatial reconstruction, the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We adopt the most compact form of CT, which requires the field be represented by area-averages at cell faces. We demonstrate that the fluxes of the area-averaged field used by CT can be made consistent with the fluxes of the volume-averaged field returned by a Riemann solver if they obey certain simple relationships. We use these relationships to derive new algorithms for constructing the CT fluxes at grid cell corners which reduce exactly to the equivalent one-dimensional solver for plane-parallel, grid-aligned flow. We show that the PPM reconstruction algorithm must include multidimensional terms for MHD, and we describe a number of important extensions that must be made to CTU in order for it to be used for MHD with CT. We present the results of a variety of test problems to demonstrate the method is accurate and robust.