Uniformly high order accurate essentially non-oscillatory schemes, III

Harten, A.; Engquist, Björn; Osher, Stanley; Chakravarthy, Sukumar

doi:10.1016/0021-9991(87)90031-3

Cited by 2,585 publications

(899 citation statements)

References 18 publications

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“…Regular meshes provide for ease of analysis and thus high order methods such as PPM (Woodward & Collela 1984) and TVD schemes (e.g. Harten et al 1987, Kurganov & Tadmor 2000 have been developed. The inner loops of mesh methods can often be pipelined for high performance.…”

Section: Gasdynamicsmentioning

confidence: 99%

Gasoline: a flexible, parallel implementation of TreeSPH

2004

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The key algorithms and features of the Gasoline code for parallel hydrodynamics with self-gravity are described. Gasoline is an extension of the efficient Pkdgrav parallel N -body code using smoothed particle hydrodynamics. Accuracy measurements, performance analysis and tests of the code are presented. Recent successful Gasoline applications are summarized. These cover a diverse set of areas in astrophysics including galaxy clusters, galaxy formation and gas-giant planets. Future directions for gasdynamical simulations in astrophysics and code development strategies for tackling cutting edge problems are discussed.

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Section: Gasdynamicsmentioning

confidence: 99%

Gasoline: a flexible, parallel implementation of TreeSPH

2004

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“…MM2 for the minmod, MC2 for monotonized centered). For r > 2 we have a choice of ENO-like routines: ENO3 for the thirdorder original ENO method (Harten et al 1987), CENO3 for the convex-ENO scheme by Liu & Osher (1998, see also Paper I) , WENO5 for the weighted-ENO fifth-order scheme (Jiang & Shu 1996). Moreover, in the tests of Sects.…”

Section: Lr Xmentioning

confidence: 99%

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

Zanna¹,

Zanotti²,

Bucciantini

et al. 2007

A&A

316

448

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Aims. We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent threedimensional 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 Alfvén 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.

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“…rd -order ENO [60] interpolation in space and 2 nd -order ENO interpolation in time are used. The prolonged and restricted variables are the conserved evolved ones: D, S i , and τ .…”

Section: E Adaptive Mesh Refinementmentioning

confidence: 99%

Binary neutron-star mergers with Whisky and SACRA: First quantitative comparison of results from independent general-relativistic hydrodynamics codes

Baiotti

Shibata

Yamamoto³

2010

Phys. Rev. D

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We present the first quantitative comparison of two independent general-relativistic hydrodynamics codes, the Whisky code and the SACRA code. We compare the output of simulations starting from the same initial data and carried out with the configuration (numerical methods, grid setup, resolution, gauges) which for each code has been found to give consistent and sufficiently accurate results, in particular in terms of cleanness of gravitational waveforms. We focus on the quantities that should be conserved during the evolution (rest mass, total mass energy, and total angular momentum) and on the gravitational-wave amplitude and frequency. We find that the results produced by the two codes agree at a reasonable level, with variations in the different quantities but always at better than about 10%.

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Uniformly high order accurate essentially non-oscillatory schemes, III

Cited by 2,585 publications

References 18 publications

Gasoline: a flexible, parallel implementation of TreeSPH

Gasoline: a flexible, parallel implementation of TreeSPH

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

Binary neutron-star mergers with Whisky and SACRA: First quantitative comparison of results from independent general-relativistic hydrodynamics codes

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