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

Balsara, Dinshaw S.; Spicer, D. S.

doi:10.1006/jcph.1998.6153

Cited by 587 publications

(712 citation statements)

References 26 publications

(41 reference statements)

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“…Balsara and Spicer [7] do treat more general geometries for the ideal MHD case and the results developed here can also be easily extended to general geometries. Notice that in eqns.…”

Section: I) Introductionmentioning

confidence: 98%

“…(1.1) be discretized in a conservative fashion. Loss of divergence-free evolution has been shown to result in unphysical solutions by several authors, for example see Balsara and Spicer [7] and Toth [43]. Brackbill and Barnes [14] and Brackbill [15] have shown that violating the £ ¤ = 0 B constraint leads to unphysical plasma transport orthogonal to the magnetic field as well as a loss of momentum and energy conservation.…”

Section: I) Introductionmentioning

confidence: 99%

“…II) Review and Extension of the Numerical MHD Scheme of Balsara and Spicer [7] 7 Balsara and Spicer [7] constructed a divergence-free scheme for ideal MHD. In this section we recapitulate the essentials of their scheme while at the same time showing that it can be naturally extended to resistive, non-ideal MHD.…”

Section: I) Introductionmentioning

confidence: 99%

“…(2.1) becomes : The Balsara and Spicer [7] scheme is based on realizing that there is a dualism between the fluxes that are produced by a higher order Godunov scheme and the electric fields that are needed in eqn. (1.2).…”

Section: I) Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

Balsara

2001

Journal of Computational Physics

250

329

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“…Balsara and Spicer [7] do treat more general geometries for the ideal MHD case and the results developed here can also be easily extended to general geometries. Notice that in eqns.…”

Section: I) Introductionmentioning

confidence: 98%

Section: I) Introductionmentioning

confidence: 99%

Section: I) Introductionmentioning

confidence: 99%

Section: I) Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

Balsara

2001

Journal of Computational Physics

250

329

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“…These combined fluxes at face centers, f (n ) x,i+1/2,j,k , f (n ) y ,i,j +1/2,k , and f (n ) z ,i,j,k+1/2 , are used to enforce ∇ · B = 0 as well as to update the magnetic field components to the next time step, as the advection only fluxes for the ideal MHD case do. In fact, we used the fluxinterpolated CT (Constraint Transport) scheme developed in Balsara & Spicer(1999).…”

Section: Ad Mhd Equations and Numerical Methodsmentioning

confidence: 99%

A Fast Explicit Scheme for Solving MHD Equations with Ambipolar Diffusion

Kim

2010

Proc. IAU

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Abstract. We developed a fast numerical scheme for solving ambipolar diffusion MHD equations with the strong coupling approximation, which can be written as the ideal MHD equations with an additional ambipolar diffusion term in the induction equation. The mass, momentum, magnetic fluxes due to the ideal MHD equations can be easily calculated by any Godunovtype schemes. Additional magnetic fluxes due to the ambipolar diffusion term are added in the magnetic fluxes, because of two same spatial gradients operated on the advection fluxes and the ambipolar diffusion term. In this way, we easily kept divergence-free magnetic fields using the constraint transport scheme. In order to overcome a small time step imposed by ambipolar diffusion, we used the super time stepping method. The resultant scheme is fast and robust enough to do the long term evolution of star formation simulations. We also proposed that the decay of alfven by ambipolar diffusion be a good test problem for our codes.

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Amplification of magnetic fields by supernova‐driven turbulence

Kim

Balsara

2006

Astron Nachr

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Observations of µG magnetic fields in radio galaxies at cosmological epochs as early as around z = 2 have shortened the available time for dynamo action. This fact suggests that the mean-field dynamo mechanism in a global galactic scale either is too slow to amplify a seed field generated by the Biermann battery effect to the level of the observed field strength at z ∼ 2 or needs much stronger seed fields of an order of 10 −10 G. A "contamination" picture that amplified magnetic fields in smaller objects, such as stars or AGNs, within a relatively shorter timescale spread out through supernova ejecta, stellar winds, and AGN jets to nearby environments is gaining momentum. In line with this picture, we demonstrate, through three-dimensional numerical experiments, that magnetic fields can be amplified by supernova-driven turbulence with two orders of magnitude smaller e-folding timescale than that of the mean-field dynamo mechanism. Therefore, supernova-driven turbulence may play an important role in amplifying small-scale B-fields in any astrophysical systems that have harbored massive stars.

show abstract

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

Cited by 587 publications

References 26 publications

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

A Fast Explicit Scheme for Solving MHD Equations with Ambipolar Diffusion

Amplification of magnetic fields by supernova‐driven turbulence

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