Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

Balsara, Dinshaw S.

doi:10.1006/jcph.2001.6917

Cited by 250 publications

(342 citation statements)

References 49 publications

(115 reference statements)

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“…Following the method described in Refs. [47,48], we employ a divergence-free-preserving interpolation based on WENO5 [58]. In Appendix A, the grid structure, the scheme for integrating the induction equation, as well as the prolongation/restriction schemes of magnetic fields are described in details.…”

Section: A Formulation and Numerical Issuementioning

confidence: 99%

“…A 1, we exploit the divergence-free reconstruction scheme in the refinement boundaries of the FMR algorithm, following Refs. [47,48]. First, we review how to reconstruct the magnetic field in the whole region of a cell in this scheme.…”

Section: Fmr Implementationmentioning

confidence: 99%

“…We follow Ref. [47] to determine these coefficients. By minimizing the magnetic energy involved in the cell with respect to a x xxy and a y xyy , we obtain…”

Section: Fmr Implementationmentioning

confidence: 99%

“…In the second approach, the hyperbolic divergence-cleaning prescription is employed to ensure the divergence-free condition of magnetic fields [26,42]. The third one [24] is based on the Balsara's constrained-transport scheme, in which a special interpolation scheme in the refinement boundaries is mandatory to preserve the divergence-free condition and the magnetic-flux conservation [47,48]. We construct a new GRMHD code employing the third approach (modifying the original scheme for the use in the vertexcentered grid) to precisely guarantee the divergence-free condition and the magnetic-flux conservation.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional evolution of differentially rotating magnetized neutron stars

2012

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We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara [47]. Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding [36] obtained in axisymmetric simulations.

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Section: A Formulation and Numerical Issuementioning

confidence: 99%

Section: Fmr Implementationmentioning

confidence: 99%

“…We follow Ref. [47] to determine these coefficients. By minimizing the magnetic energy involved in the cell with respect to a x xxy and a y xyy , we obtain…”

Section: Fmr Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-dimensional evolution of differentially rotating magnetized neutron stars

2012

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“…There are many existing AMR codes including FLASH [6], AMRVAC [7], PLUTO [8], SFUMATO [9], NIRVANA [10,11], RAMSES [12], RIEMANN [13], CRASH [14], CHARM [15], CASTRO [16,17] and so on. Some of them, e.g.…”

Section: Introductionmentioning

confidence: 99%

A new MHD code with adaptive mesh refinement and parallelization for astrophysics

Jiang

Fang

Chen

2012

Computer Physics Communications

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A new code, named MAP, is written in FORTRAN language for magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for computing the MHD part, namely, modified Mac Cormack Scheme (MMC), Lax-Fridrichs scheme (LF) and weighted essentially non-oscillatory (WENO) scheme. All of them are second order, twostep, component-wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann solvers are also equipped. A high resolution can be achieved by the hierarchical block-structured AMR mesh. We use the extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced by the scheme in the magnetic induction equation. The numerical algorithms for the non-ideal terms, e.g., the resistivity and the thermal conduction, are also equipped in the MAP code. The details of the AMR and MPI algorithms are described in the paper.

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Simulations of Jets from Active Galactic Nuclei and Gamma‐Ray Bursts

Aloy

Mimica

2012

Relativistic Jets From Active Galactic Nuclei

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Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

Cited by 250 publications

References 49 publications

Three-dimensional evolution of differentially rotating magnetized neutron stars

Three-dimensional evolution of differentially rotating magnetized neutron stars

A new MHD code with adaptive mesh refinement and parallelization for astrophysics

Simulations of Jets from Active Galactic Nuclei and Gamma‐Ray Bursts

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