ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics

By L. Del Zanna, Olindo Zanotti, N. Bucciantini, Pasquale Londrillo. 2007

286 citations recorded by the source corpus.

Aims. We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods. Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results. ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude , circularly polarized Alfven waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a fixed 5-point stencil gives highly accurate results for smooth solutions, both in flat and curved metric (up to the nominal fifth order), while at the same time providing sharp profiles in tests involving discontinuities.

Subfields: Computational Mechanics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/468412c0c0df00d30690f55514d5a6690b22cbb3

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Citations in the corpus

Beyond second-order convergence in simulations of binary neutron stars in full general-relativity (2013, methodology): “…a polytropic EOS withK = 123.56 andΓ = 2, while the evolution is performed using the ideal-fluid EOS with thesame Γ. 1 Other high-order general-relativistic hydrodynamic codes have been developed, such asWHAM (Tchekhovskoy et al. 2007) orECHO (Del Zanna et al. 2007; Bucciantini & Del Zanna 2011).”
THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics (2012, methodology): “…the development of high-order finite-volume (Tchekhovskoy et al. 2007; Duffell & MacFadyen 2011) and finite-difference (Zhang & MacFadyen 2006; Del Zanna et al. 2007) schemes, but many alternative approaches have been also proposed, including finite-element methods (Mann 1985; Meier 1999),…”
Magnetized relativistic jets and long-duration GRBs from magnetar spin-down during core-collapse supernovae (2009, methodology): “1 IN T RO D U C T I O N Observations of long-duration gamma-ray bursts (LGRBs) have demonstrated that they are associated with core-collapse supernovae (SNe) and the death of massive stars (Della Valle 2006; Woosley & Bloom 2006; Zhang 2007).”
The Einstein Toolkit: a community computational infrastructure for relativistic astrophysics (2011, background): “, [199, 200]), but have yet to be implemented widely in many branches of numerical relativity.”
The black hole accretion code (2016, methodology): “In addition to the 1D scheme, we have implemented the “2DW” method of [52, 116].”
DIRECT CALCULATION OF THE RADIATIVE EFFICIENCY OF AN ACCRETION DISK AROUND A BLACK HOLE (2008, background): “…1999; Gammie et al. 2003; De Villiers & Hawley 2003; Duez et al. 2005; Shibata & Sekiguchi 2005; Anninos et al. 2005; Antón et al. 2006; Noble et al. 2006; Mizuno et al. 2006; Anderson et al. 2006; Tchekhovskoy et al. 2007; Fragile et al. 2007; Del Zanna et al. 2007; Cerdá-Durán et al. 2008).”
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project (2019, methodology): “Software:Athena++ (White et al. 2016); BHAC (Porth et al. 2017); Cosmos++, (Anninos et al. 2005; Fragile et al. 2012, 2014); ECHO (Del Zanna et al. 2007); H-AMR (Liska et al. 2018a; Chatterjee et al. 2019); HARM-Noble (Gammie et al. 2003; Noble et al. 2006, 2009); iharm3D (Gammie et al. 2003; Noble…”
Beyond ideal MHD: towards a more realistic modelling of relativistic astrophysical plasmas (2008, methodology): “The exact solution in the ideal-MHD limit and assuming vx = 0 for simplicity, is given by (Del Zanna et al. 2007) (By, Bz) = ηAB0 (cos[k(x− vA t)], sin[k(x− vA t)]) , (vy, vz) = − vA B0 (By , Bz) , (62) whereBx = B0, k is the wave vector,ηA is the amplitude of the wave and the special relativistic A”
The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers (2020, methodology): “For example, GENESIS (Aloy et al. 1999) and Enzo (Bryan et al. 2014; Wang et al. 2008) perform a 1D iteration on pressure, the initial implementation of HARM uses the 5D method (Gammie et al. 2003), ECHO (Del Zanna et al. 2007) uses a velocity-based 1D method, RAMSES (Teyssier 2002; Lamberts et al. ”
Numerical simulations of super-critical black hole accretion flows in general relativity (2013, methodology): “In the last decade a number of such codes were developed (e.g., De Villiers et al. 2003; Gammie et al. 2003; Anninos et al. 2005; Del Zanna et al. 2007).”
Global simulations of axisymmetric radiative black hole accretion discs in general relativity with a mean-field magnetic dynamo (2014, unknown): “Optically thin flows have been extensively studied by means of general relativistic (GR) magnetohydrodynamical (MHD) simulations (e.g., De Villiers et al. 2003; Gammie et al. 2003; Anninos et al. 2005; Del Zanna et al. 2007; Narayan et al. 2012; McKinney et al. 2012; Tchekhovskoy & McKinney 2012).”
Semi-implicit scheme for treating radiation under M1 closure in general relativistic conservative fluid dynamics codes (2012, methodology): “The low optical depth and the extreme radiative inefficiency of an ADAF are a major advantage for simulations since they allow one to solve the fluid dynamics separately from the radiation field.1 A number of sophisticated GR magnetohydrodynamic (GRMHD) codes have been developed (e.g. De Villiers-P.”
Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code HARMRAD with M1 closure (2013, methodology): “(viii) Bi, v j at cell faces are interpolated to cell centers and to the corner of each 2D plane passing through the cell center. c© 2013 RAS, MNRAS 000, 1–36 (ix) Godunov EMF flux is computed using 4-state Riemann LAXF/HLL solution using Bi, v j at corners (Del Zanna et al. 2007).”