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

  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},

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

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


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…

An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics


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

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

  • Xueshang Feng
  • Physics
    Magnetohydrodynamic 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…



Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for multidimensional flow

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation…

A Divergence-free Upwind Code for Multidimensional Magnetohydrodynamic Flows

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

A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations

This paper presents a staggered mesh strategy which directly uses the properly upwinded fluxes that are provided by a Godunov scheme, and shows that a scheme that involves a collocation of magnetic field variables that is different from the one traditionally favored in the design of higher orderGodunov schemes can nevertheless offer the same robust and accurate performance.

The βˆ‡Β·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes

Based on a large number of tests, the projection scheme, one of the new central difference based schemes, and the constrained transport schemes are found to be the most accurate and reliable among the examined methods.

Total Variation Diminishing Scheme for Adiabatic and Isothermal Magnetohydrodynamics

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…

Extension of the Piecewise Parabolic Method to Multidimensional Ideal Magnetohydrodynamics

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…

An approximate Riemann solver for ideal magnetohydrodynamics

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…

High-Order Upwind Schemes for Multidimensional Magnetohydrodynamics

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

A Higher-Order Godunov Method for Multidimensional Ideal Magnetohydrodynamics

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.