An HLLC Riemann solver for resistive relativistic magnetohydrodynamics

Aranguren, S. Miranda; Aloy, M. Á.; Rembiasz, Tomasz

doi:10.1093/mnras/sty419

Cited by 22 publications

(21 citation statements)

References 145 publications

(240 reference statements)

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“…However, two distinct phases can be discerned using the MHLLC solver: a steeper growth for t 6 − 8 followed by a softer one for t 6 − 8, the actual value depending on the resolution. The behavior remains unaltered when switching from CT to GLM and it is not observed by Del and Miranda-Aranguren et al (2018) who used 5th or higher-order reconstructions. For our second-order scheme, instead, we attribute this behavior to compressible effects enhanced by the resolution of density jumps, probably triggering spurious modes that grow faster in the early stage of evolution.…”

Section: Tearing Modementioning

confidence: 79%

“…The shock-tube problem is a standard numerical benchmark consisting of an initial discontinuity separating two constant states. Here we adopt a configuration similar to the one presented in Palenzuela et al (2009);Dionysopoulou et al (2013);Miranda-Aranguren et al (2018) and assign 1D left and right states as…”

Section: Rotated Shock-tubementioning

confidence: 99%

“…Overall, the CT scheme performs similarly to the GLM method albeit with slightly reduced numerical dissipation and better convergence with resolution. Perturbations are expected to grow exponentially as Q 1 ∝ e γ T M t and we have measured the numerical growth rate by considering, as suggested by Miranda-Aranguren et al (2018), the integral of the x-component of magnetic field (squared),…”

Section: Tearing Modementioning

confidence: 99%

“…More recently several authors have discussed schemes for the numerical solution of such system of equations and have presented actual implementations (see, e.g. Komissarov 2007;Dumbser & Zanotti 2009;Palenzuela et al 2009;Takamoto & Inoue 2011;Bucciantini & Del Zanna 2013;Dionysopoulou et al 2013;Mizuno 2013;Miranda-Aranguren et al 2018).…”

Section: Introductionmentioning

confidence: 99%

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A constrained transport method for the solution of the resistive relativistic MHD equations

Mignone

Mattia

Bodo

et al. 2019

Monthly Notices of the Royal Astronomical Society

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We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces and are evolved using the constrained transport formalism. Direct application of Stokes' theorem to Faraday's and Ampere's laws ensures that the resulting discretization is divergence-free for the magnetic field and charge-conserving for the electric field. Hydrodynamic variables retain, instead, the usual zone-centred representation commonly adopted in finite-volume schemes. Temporal discretization is based on Runge-Kutta implicit-explicit (IMEX) schemes in order to resolve the temporal scale disparity introduced by the stiff source term in Ampere's law. The implicit step is accomplished by means of an improved and more efficient Newton-Broyden multidimensional rootfinding algorithm. The explicit step relies on a multidimensional Riemann solver to compute the line-averaged electric and magnetic fields at zone edges and it employs a one-dimensional Riemann solver at zone interfaces to update zone-centred hydrodynamic quantities. For the latter, we introduce a five-wave solver based on the frozen limit of the relaxation system whereby the solution to the Riemann problem can be decomposed into an outer Maxwell solver and an inner hydrodynamic solver. A number of numerical benchmarks demonstrate that our method is superior in stability and robustness to the more popular charge-conserving divergence cleaning approach where both primary electric and magnetic fields are zone-centered. In addition, the employment of a less diffusive Riemann solver noticeably improves the accuracy of the computations.

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Section: Tearing Modementioning

confidence: 79%

Section: Rotated Shock-tubementioning

confidence: 99%

Section: Tearing Modementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A constrained transport method for the solution of the resistive relativistic MHD equations

Mignone

Mattia

Bodo

et al. 2019

Monthly Notices of the Royal Astronomical Society

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“…Note that a multidimensional Riemann solver for the SRRMHD equations was recently presented by Mignone et al (2018Mignone et al ( , 2019 and Miranda-Aranguren et al (2018).…”

Section: Characteristic Speedmentioning

confidence: 99%

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations

Ripperda

Bacchini

Porth

et al. 2019

ApJS

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Recent advances in black hole astrophysics, particularly the first visual evidence of a supermassive black hole at the center of the galaxy M87 by the Event Horizon Telescope, and the detection of an orbiting "hot spot" nearby the event horizon of Sgr A * in the Galactic center by the Gravity Collaboration, require the development of novel numerical methods to understand the underlying plasma microphysics. Non-thermal emission related to such hot spots is conjectured to originate from plasmoids that form due to magnetic reconnection in thin current layers in the innermost accretion zone. Resistivity plays a crucial role in current sheet formation, magnetic reconnection, and plasmoid growth in black hole accretion disks and jets. We included resistivity in the three-dimensional generalrelativistic magnetohydrodynamics (GRMHD) code BHAC and present the implementation of an implicit-explicit scheme to treat the stiff resistive source terms of the GRMHD equations. The algorithm is tested in combination with adaptive mesh refinement to resolve the resistive scales and a constrained transport method to keep the magnetic field solenoidal. Several novel methods for primitive-variable recovery, a key part in relativistic magnetohydrodynamics codes, are presented and compared for accuracy, robustness, and efficiency. We propose a new inversion strategy that allows for resistive-GRMHD simulations of low gas-to-magnetic pressure ratio and highly magnetized regimes as applicable for black hole accretion disks, jets, and neutron-star magnetospheres. We apply the new scheme to study the effect of resistivity on accreting black holes, accounting for dissipative effects as reconnection.

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Cell-Centered Finite Volume Methods

Feng

2019

Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere

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An HLLC Riemann solver for resistive relativistic magnetohydrodynamics

Cited by 22 publications

References 145 publications

A constrained transport method for the solution of the resistive relativistic MHD equations

A constrained transport method for the solution of the resistive relativistic MHD equations

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations

Cell-Centered Finite Volume Methods

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