### Citations

1465 |
Fluid Mechanics
- LD, EM
- 1959
(Show Context)
Citation Context ...in Section (8) together with an outlook for future developments. Finally, some additional technical information is presented in Section (9). The reader is assumed to have basic knowledge in classical =-=[91, 34]-=- and relativistic fluid dynamics [166, 6], as well as in finite difference/volume methods for partial differential equations [148, 129]. A discussion of modern finite volume methods for hyperbolic sys... |

596 |
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 2nd Edition
- Toro
- 1999
(Show Context)
Citation Context ...ct Riemann solver in a numerical code. These methods are written in conservation form and use different procedures (Riemann solvers) to compute approximations to u(0; unj , u n j+1). The book of Toro =-=[171]-=- gives a comprehensive overview of numerical methods based on Riemann solvers. The numerical dissipation required to stabilize an algorithm across discontinuities can also be provided by adding local ... |

131 | Numerical Simulation of Reactive Flow, - Oran, Boris - 1987 |

118 |
2000 Astrophys
- Narayan
(Show Context)
Citation Context ...the GRB) [21, 1]. From optical spectra thus obtained redshifts of several gamma–ray bursts have been determined, e.g.,GRB970508 (z = 0.835 [113, 137]), GRB971214 (z = 3.42 [86]), GRB980703 (z = 0.966 =-=[40]-=-) and GRB990123 (1.60 ≤ z < 2.05 [5]), which confirm that (at least some) GRBs occur at cosmological distances. Assuming isotropic emission the inferred total energy of cosmological GRBs emitted in fo... |

73 |
Computational Gasdynamics
- Laney
(Show Context)
Citation Context ...l as in finite difference/volume methods for partial differential equations [148, 129]. A discussion of modern finite volume methods for hyperbolic systems of conservation laws can be found, e.g., in =-=[95, 96, 92]-=-. The theory of spectral methods for fluid dynamics is developed in [23], and smoothed particle hydrodynamics (SPH) is reviewed in [119]. 2 SPECIAL RELATIVISTIC HYDRO-DYNAMICS 2.1 Equations Using the ... |

67 |
R A 1977 Astrophys
- Bahcall, Wolf
(Show Context)
Citation Context ...in the energies released in a GRB various catastrophic collapse events have been proposed including neutron–star/neutron–star mergers [131, 69, 48], neutron– star/black–hole mergers [117], collapsars =-=[187, 98]-=- and hypernovae [132]. These models all rely on a common engine, namely a stellar mass black hole which accretes several solar masses of matter from a disk (formed during a merger or by a non–spherica... |

58 |
Numerical Methods for Conservation
- LeVeque
- 1992
(Show Context)
Citation Context ...l as in finite difference/volume methods for partial differential equations [148, 129]. A discussion of modern finite volume methods for hyperbolic systems of conservation laws can be found, e.g., in =-=[95, 96, 92]-=-. The theory of spectral methods for fluid dynamics is developed in [23], and smoothed particle hydrodynamics (SPH) is reviewed in [119]. 2 SPECIAL RELATIVISTIC HYDRO-DYNAMICS 2.1 Equations Using the ... |

50 |
Relativistic Fluids and Magneto-fluids
- Anile
- 1990
(Show Context)
Citation Context ...or future developments. Finally, some additional technical information is presented in Section (9). The reader is assumed to have basic knowledge in classical [91, 34] and relativistic fluid dynamics =-=[166, 6]-=-, as well as in finite difference/volume methods for partial differential equations [148, 129]. A discussion of modern finite volume methods for hyperbolic systems of conservation laws can be found, e... |

50 |
Astrophys
- Goodman
- 1983
(Show Context)
Citation Context ...f GRB980425 and SN1998bw is extremely low [138]. In order to explain the energies released in a GRB various catastrophic collapse events have been proposed including neutron–star/neutron–star mergers =-=[131, 69, 48]-=-, neutron– star/black–hole mergers [117], collapsars [187, 98] and hypernovae [132]. These models all rely on a common engine, namely a stellar mass black hole which accretes several solar masses of m... |

37 |
Computational
- Potter
- 1973
(Show Context)
Citation Context ...on (9). The reader is assumed to have basic knowledge in classical [91, 34] and relativistic fluid dynamics [166, 6], as well as in finite difference/volume methods for partial differential equations =-=[148, 129]-=-. A discussion of modern finite volume methods for hyperbolic systems of conservation laws can be found, e.g., in [95, 96, 92]. The theory of spectral methods for fluid dynamics is developed in [23], ... |

32 | Astrophys - Wilson - 1990 |

19 |
Astrophys
- Krasnopolsky, Li, et al.
- 1999
(Show Context)
Citation Context ...ng, appear to be highly collimated with a bright spot (the core) at one end of the jet and a series of components which separate from the core, sometimes at superluminal speeds. In the standard model =-=[16]-=-, these speeds are interpreted as a consequence of relativistic bulk motions in jets propagating at small angles to the line of sight with Lorentz factors up to 20 or more. Moving components in these ... |

13 |
in Numerical Modelling of Nonlinear Stellar
- Benz
- 1990
(Show Context)
Citation Context ... is a free-Lagrange method, i.e., spatial gradients are evaluated without the use of a computational grid. A comprehensive discussion of SPH can be found in the reviews of Hernquist & Katz [76], Benz =-=[11]-=- and Monaghan [118, 119]. The non-relativistic SPH equations are briefly discussed in Section (9.5). The capabilities and limits of SPH are explored, e.g., in [164, 167], and the stability of the SPH ... |

10 |
Nature 355
- Meegan, Fishman, et al.
- 1992
(Show Context)
Citation Context ...rces major progress has occured through the observations by the BATSE detector on board the Compton Gamma–Ray Observatory (GRO), which have proven that GRBs are distributed isotropically over the sky =-=[111]-=-. Even more important the detection and the rapid availability of accurate coordinates (∼ arc minutes) of the fading X–ray counterparts of GRBs by the BeppoSAX spacecraft beginning in 1997 [33, 143] h... |

6 |
Astron. Astrophys
- Steinmetz, Müller
- 1993
(Show Context)
Citation Context ...es associated to the SRHD system in 3D has been first derived by Donat et al. [42]. Previously, Mart́ı et al. . [104] obtained the spectral decomposition in 1D SRHD and Eulderink [50] and Font et al. =-=[58]-=-, the (eigenvalues and) right eigenvectors in 3D. The Jacobians are given by Bi = ∂F i(u) ∂u , (67) where the state vector u and the flux vector Fi are defined in (6) and (7), respectively. In the fol... |

6 |
Astron. Astrophys
- Piro, Heise, et al.
- 1998
(Show Context)
Citation Context ...e sky [111]. Even more important the detection and the rapid availability of accurate coordinates (∼ arc minutes) of the fading X–ray counterparts of GRBs by the BeppoSAX spacecraft beginning in 1997 =-=[33, 143]-=- has allowed for subsequent successful ground based observations of faint GRB afterglows at optical and radio wavelength. In case of GRB990123 the optical, X–ray and gamma–ray emission was detected fo... |

6 |
Methods for Initial–value Problems
- Richtmyer, Morton
- 1967
(Show Context)
Citation Context ...dynamics (SRHD) was made by Wilson [183, 184] and collaborators [27, 75] using an Eulerian explicit finite difference code with monotonic transport. The code relies on artificial viscosity techniques =-=[181, 150]-=- to handle shock waves. It has been widely used to simulate flows encountered in cosmology, axisymmetric relativistic stellar collapse, accretion onto compact objects and, more recently, collisions of... |

5 |
Nature 393
- Kulkarni, Djorgovski, et al.
- 1998
(Show Context)
Citation Context ... seconds after the onset of the GRB) [21, 1]. From optical spectra thus obtained redshifts of several gamma–ray bursts have been determined, e.g.,GRB970508 (z = 0.835 [113, 137]), GRB971214 (z = 3.42 =-=[86]-=-), GRB980703 (z = 0.966 [40]) and GRB990123 (1.60 ≤ z < 2.05 [5]), which confirm that (at least some) GRBs occur at cosmological distances. Assuming isotropic emission the inferred total energy of cos... |

4 | A Particle Method for Relativistic Fluid Dynamics - Lahy - 1989 |

4 |
MHD in Divergence Form: A Computational Method for Astrophysical Flow
- Putten
- 1992
(Show Context)
Citation Context ...scillations in the case of strong shocks and a smoothing algorithm should be applied. Details of this smoothing algorithm and of the numerical method in one and two spatial dimensions can be found in =-=[174]-=- together with results on a large variety of tests. Van Putten has applied his method to simulate relativistic hydrodynamic and magneto hydrodynamic jets with moderately flow Lorentz factors (< 4.25) ... |

3 |
Saas-Fee Advanced Course 20. Active galactic nuclei
- Blandford, Netzer, et al.
- 1990
(Show Context)
Citation Context ...ollimated at subparsec scales. Current theoretical models assume that accretion disks are the source of the bipolar outflows which are further collimated and accelerated via MHD processes (see, e.g., =-=[15]-=-). There is a large number of parameters which are potentially important for jet powering: the black hole mass and spin, the accretion rate and the type of accretion disk, the properties of the magnet... |

3 |
Astrophys
- Pian, Fruchter, et al.
- 1998
(Show Context)
Citation Context ...ly (optical observations began 22 seconds after the onset of the GRB) [21, 1]. From optical spectra thus obtained redshifts of several gamma–ray bursts have been determined, e.g.,GRB970508 (z = 0.835 =-=[113, 137]-=-), GRB971214 (z = 3.42 [86]), GRB980703 (z = 0.966 [40]) and GRB990123 (1.60 ≤ z < 2.05 [5]), which confirm that (at least some) GRBs occur at cosmological distances. Assuming isotropic emission the i... |

2 |
in Relativistic Astrophysics
- Camenzind
- 1998
(Show Context)
Citation Context ...ese sources, although with smaller values of the overall bulk speeds [20]. Although MHD and general relativistic effects seem to be crucial for a successful launch of the jet (for a review see, e.g., =-=[22]-=-), purely hydrodynamic, special relativistic simulations are adequate to study the morphology and dynamics of relativistic jets at distances sufficiently far from the central compact object (i.e., at ... |

2 |
Astrophys
- Koide
- 1997
(Show Context)
Citation Context ...stic information. This last fact makes the algorithm extremely simple when applied to any hyperbolic system of conservation laws. A relativistic version of Davis’ method has been used by Koide et al. =-=[81, 80, 126]-=- in 2D and 3D simulations of relativistic magneto–hydrodynamic jets with moderate Lorentz factors. Although the results obtained are encouraging, the coarse grid zoning used in these simulations and t... |

2 |
Nature 395
- Kulkarni, Frail, et al.
- 1998
(Show Context)
Citation Context ...within the 8 arc minute error box of GRB980425 [161, 138]. Its explosion time is consistent with that of the GRB, and relativistic expansion velocities are derived from radio observations of SN1998bw =-=[87]-=-. BeppoSAX detected two fading X–ray sources within the error box, one being positionally consistent with the supernova and a fainter one not consistent with the position of SN1998bw [138]. Taken toge... |

2 |
Astrophys
- Pacyński
- 1998
(Show Context)
Citation Context ...f GRB980425 and SN1998bw is extremely low [138]. In order to explain the energies released in a GRB various catastrophic collapse events have been proposed including neutron–star/neutron–star mergers =-=[131, 69, 48]-=-, neutron– star/black–hole mergers [117], collapsars [187, 98] and hypernovae [132]. These models all rely on a common engine, namely a stellar mass black hole which accretes several solar masses of m... |

2 |
Astron. Astrophys
- Pons, Font, et al.
- 1998
(Show Context)
Citation Context ...an exact relativistic Riemann solver with non-zero transverse speeds. e there exist GRHD extensions of several HRSC methods based on linearized Riemann solvers. The procedure developed by Pons et al. =-=[146]-=- allows any SRHD Riemann solver to be applied to GRHD flows. f except HLL which requires spectral decomposition of RMHD equations or solution of RMHD Riemann problem. Van Putten [180] has studied the ... |

1 |
in Numerical Methods for Fluid Dynamics 4, eds. K.W.Morton and M.J.Baines
- Falle, Giddings
- 1993
(Show Context)
Citation Context ...tion AMRA of Plewa [144]. Komissarov & Falle [84] have combined their numerical scheme with the adaptive grid code, Cobra, which has been developed by Mantis Numerics Ltd. for industrial applications =-=[54]-=-, and which uses a hierarchy of grids with a constant refinement factor of two between subsequent grid levels. 8.2.3 General relativistic hydrodynamics (GRHD) Up to now only very few attempts have bee... |

1 |
J.Ma and Ibáñez, J.Ma
- Gómez, Marscher, et al.
- 1998
(Show Context)
Citation Context ...the beam flow Lorentz factor at the jet inlet. The dynamic interaction between the induced traveling shocks and the underlying steady jet can account for the complex behavior observed in many sources =-=[67]-=-. The first magnetohydrodynamic simulations of relativistic jets have been already undertaken in 2D [81, 80] and 3D [125, 126] to study the implications of ambient magnetic fields in the morphology an... |

1 |
in Relativistic Fluid Dynamics, eds. A.Anile and Y.ChoquetBruhat
- Israel
- 1987
(Show Context)
Citation Context ...es the Lagrangian time derivative. Πab is the artificial viscosity tensor, which is required in SPH to handle shock waves. It poses a major obstacle in extending SPH to relativistic flows (see, e.g., =-=[77, 29]-=-). Wab is the interpolating kernel, and ∇aWab denotes the gradient of the kernel taken with respect to the coordinates of particle a. The kernel is a function of |ra − rb| (and of the SPH smoothing le... |

1 |
Astrophys
- Mart́ı, Müller, et al.
- 1997
(Show Context)
Citation Context ...relativistic flows was accomplished when high–resolution shock–capturing (HRSC) methods, specially designed to solve hyperbolic systems of conservations laws, were applied to solve the SRHD equations =-=[104, 103, 50, 51]-=-. This review is intended to provide a comprehensive discussion of different HRSC methods and of related methods used in SRHD. Numerical methods for special relativistic MHD flows are not included, be... |