On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method

Londrillo, P.; Zanna, L. Del

doi:10.1016/j.jcp.2003.09.016

Cited by 224 publications

(284 citation statements)

References 30 publications

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“…Various implementations of the CT scheme have been devised that differ mainly in the way the magnetic stress and electric field are calculated. Of these, our implementation resembles most closely the recently developed upwind-CT schemes (Londrillo & del Zanna 2004;Gardiner & Stone 2005. We obtain E from the zone interface values of the velocity and the magnetic field that are both computed by the (MUSTA) Riemann solver.…”

Section: Methodsmentioning

confidence: 99%

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

Obergaulinger¹,

Aloy

Müller³

2010

A&A

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Context. Global magnetohydrodynamic simulations show the growth of Kelvin-Helmholtz instabilities at the contact surface of two merging neutron stars. That region has been identified as the site of efficient amplification of magnetic fields. However, these global simulations, due to numerical limitations, were unable to determine the saturation level of the field strength, and thus the possible back-reaction of the magnetic field onto the flow. Aims. We investigate the amplification of initially weak magnetic fields in Kelvin-Helmholtz unstable shear flows, and the backreaction of the field onto the flow. Methods. We use a high-resolution finite-volume ideal MHD code to perform 2D and 3D local simulations of hydromagnetic shear flows, both for idealized systems and simplified models of merger flows. Results. In 2D, the magnetic field is amplified on time scales of less than 0.01 ms until it reaches locally equipartition with the kinetic energy. Subsequently, it saturates due to resistive instabilities that disrupt the Kelvin-Helmholtz unstable vortex and decelerate the shear flow on a secular time scale. We determine scaling laws of the field amplification with the initial field strength and the grid resolution. In 3D, the hydromagnetic mechanism seen in 2D may be dominated by purely hydrodynamic instabilities leading to less filed amplification. We find maximum magnetic fields ∼10 16 G locally, and rms maxima within the box ∼10 15 G. However, due to the fast decay of the shear flow such strong fields exist only for a short period (<0.1 ms). In the saturated state of most models, the magnetic field is mainly oriented parallel to the shear flow for rather strong initial fields, while weaker initial fields tend to lead to a more balanced distribution of the field energy among the components. In all models the flow shows small-scale features. The magnetic field is at most in energetic equipartition with the decaying shear flow. Conclusions. The magnetic field may be amplified efficiently to very high field strengths, the maximum field energy reaching values of the order of the kinetic energy associated with the velocity components transverse to the interface between the two neutron stars. However, the dynamic impact of the field onto the flow is limited to the shear layer, and it may not be adequate to produce outflows, because the time during which the magnetic field stays close to its maximum value is short compared to the time scale for launching an outflow (i.e., a few milliseconds).

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Section: Methodsmentioning

confidence: 99%

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

Obergaulinger¹,

Aloy

Müller³

2010

A&A

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“…Toth [45] found the flux constrained transport method was one of the most accurate schemes that he tested. This approach has been combined with various shock-capturing schemes by different researchers [6,46,47,41,[48][49][50][51][52]. In this paper, the constrained transport method proposed by Balsara and Spicer [41] is adopted.…”

Section: E-cusp Scheme For Mhd Equationsmentioning

confidence: 99%

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

Shen

Zha

Huerta

2012

Journal of Computational Physics

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a b s t r a c tAn E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices.

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“…The same procedures apply to the induction equation, where a proper staggered discretization and a specific 2D Riemann solver are needed to take into account the specific curl form of the differential operators and of the related conservation laws based on the Stokes theorem. 32 We notice that the above upwind flux reconstruction applies only to the ideal set of MHD equations.…”

Section: ͑11͒mentioning

confidence: 99%

Three-dimensional simulations of compressible tearing instability

et al. 2008

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Three-dimensional numerical simulations of the tearing instability in the framework of compressible and resistive magnetohydrodynamics are presented. Simulations have been performed with a novel Eulerian conservative high order code, including an explicit resistivity, which uses implicit high order numerical schemes having higher spectral resolution than classical schemes. The linear and non linear evolution of the tearing instability has been followed for force-free and pressure-balanced initial equilibrium configurations. Pressure equilibrium configurations are subject to a secondary instability which drives the system toward a quasi two dimensional structure oriented perpendicularly to the initial configuration. The development of secondary instabilities is suppressed by a guide field allowing the coalescence instability to fully develop in the system. Force-free initial configurations follow an intermediate path with respect the previous cases: Strong coalescence of magnetic islands, due to the non linear evolution of the tearing instability, is observed before the system enters in a phase dominated by 3D modes. The histories of the differing initial current-sheet equilibria have counterparts in the energy spectra that, for all three cases, are observed to be strongly anisotropic.

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On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method

Cited by 224 publications

References 30 publications

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

Three-dimensional simulations of compressible tearing instability

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