# An unsplit, cell-centered Godunov method for ideal MHD - eScholarship

@inproceedings{Crockett2003AnUC, title={An unsplit, cell-centered Godunov method for ideal MHD - eScholarship}, author={Robert Crockett and Phillip Colella and Robert T. Fisher and Richard Klein and Christopher F. McKee}, year={2003} }

## 120 Citations

### An unsplit Godunov method for ideal MHD via constrained transport in three dimensions

- Computer ScienceJ. Comput. Phys.
- 2008

### A second-order unsplit Godunov scheme for cell-centered MHD: The CTU-GLM scheme

- PhysicsJ. Comput. Phys.
- 2010

### AN UNSPLIT STAGGERED MESH SCHEME FOR MULTIDIMENSIONAL

- Physics
- 2007

We introduce an unsplit staggered mesh scheme (USM) that solves multidimensional magnetohydrodynamics (MHD) by a constrained transport method with high-order Godunov fluxes, incorporating three new…

### A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics

- Computer ScienceJ. Comput. Phys.
- 2013

### An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics

- PhysicsJ. Comput. Phys.
- 2009

### CONSTRAINED-TRANSPORT MAGNETOHYDRODYNAMICS WITH ADAPTIVE MESH REFINEMENT IN CHARM

- Computer Science, Physics
- 2011

A three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM is presented, based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme.

### A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical and geophysical MHD

- Computer Science
- 2007

The proposed MUSCL-Hancock scheme for Euler equations is extended to the induction equation modeling the magnetic field evolution in kinematic dynamo problems and shows its versatility by applying it to the ABC dynamo problem and to the collapse of a magnetized cloud core.

### A Finite Volume MHD Code in Spherical Coordinates for Background Solar Wind

- PhysicsMagnetohydrodynamic Modeling of the Solar Corona and Heliosphere
- 2019

A second-order Godunov-type finite volume method (FVM) to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time has been implemented into a numerical code. This…

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A description is given for preserving 𝛁 ∙ = 0 in a magnetohydrodynamic (MHD) code that employs the upwind, total variation diminishing (TVD) scheme and Strang type operator splitting for…

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In this paper a total variation diminishing (TVD) scheme is constructed for solving the equations of ideal adiabatic and isothermal MHD. It is based on an extremely efficient formulation of the MHD…

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An extension of the piecewise parabolic method to treat multidimensional ideal magnetohydrodynamical equations is presented in this paper. The multidimensional scheme is constructed from a…

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Abstract To construct numerical schemes of the Godunov type for solving magnetohydrodynamical (MHD) problems, an approximate method of solving the MHD Riemann problem is required in order to…

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A general method for constructing high-order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint 𝛁 ∙ = 0 for the…

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A higher-order Godunov method for the solution of the two- and three-dimensional equations of ideal magnetohydrodynamics (MHD) has no problems handling any of the three MHD waves, yet resolves shocks to three or four computational zones.