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Автор: Grafiati
Опубліковано: 14 березня 2023

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1

Martí, José Ma, José Ma Ibáñez, and Juan A. Miralles. "Numerical relativistic hydrodynamics: Local characteristic approach." Physical Review D 43, no. 12 (June 15, 1991): 3794–801. http://dx.doi.org/10.1103/physrevd.43.3794.

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2

van Odyck, D. E. A. "Review of numerical special relativistic hydrodynamics." International Journal for Numerical Methods in Fluids 44, no. 8 (February 24, 2004): 861–84. http://dx.doi.org/10.1002/fld.678.

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3

Jeon, Sangyong, and Ulrich Heinz. "Introduction to hydrodynamics." International Journal of Modern Physics E 24, no. 10 (October 2015): 1530010. http://dx.doi.org/10.1142/s0218301315300106.

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Анотація:
Hydrodynamics has been successful in providing a good description of the bulk dynamics in ultra-relativistic heavy ion collisions. In this brief review, we provide basics of the theory of viscous hydrodynamics. Topics covered include derivation of the 2nd order viscous hydrodynamics from the linear response theory and kinetic theory, viscous anisotropic hydrodynamics, and numerical implementation of relativistic hydrodynamics.
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4

Chabanov, Michail, Luciano Rezzolla, and Dirk H. Rischke. "General-relativistic hydrodynamics of non-perfect fluids: 3+1 conservative formulation and application to viscous black hole accretion." Monthly Notices of the Royal Astronomical Society 505, no. 4 (May 17, 2021): 5910–40. http://dx.doi.org/10.1093/mnras/stab1384.

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ABSTRACT We consider the relativistic hydrodynamics of non-perfect fluids with the goal of determining a formulation that is suited for numerical integration in special-relativistic and general-relativistic scenarios. To this end, we review the various formulations of relativistic second-order dissipative hydrodynamics proposed so far and present in detail a particular formulation that is fully general, causal, and can be cast into a 3+1 flux-conservative form, as the one employed in modern numerical-relativity codes. As an example, we employ a variant of this formulation restricted to a relaxation-type equation for the bulk viscosity in the general-relativistic magnetohydrodynamics code bhac. After adopting the formulation for a series of standard and non-standard tests in 1+1-dimensional special-relativistic hydrodynamics, we consider a novel general-relativistic scenario, namely, the stationary, spherically symmetric, viscous accretion on to a black hole. The newly developed solution – which can exhibit even considerable deviations from the inviscid counterpart – can be used as a testbed for numerical codes simulating non-perfect fluids on curved backgrounds.
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5

Ryu, Dongsu, Indranil Chattopadhyay, and Eunwoo Choi. "Equation of State in Numerical Relativistic Hydrodynamics." Astrophysical Journal Supplement Series 166, no. 1 (September 2006): 410–20. http://dx.doi.org/10.1086/505937.

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6

Millmore, S. T., and I. Hawke. "Numerical simulations of interfaces in relativistic hydrodynamics." Classical and Quantum Gravity 27, no. 1 (December 15, 2009): 015007. http://dx.doi.org/10.1088/0264-9381/27/1/015007.

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7

Schneider, V., U. Katscher, D. H. Rischke, B. Waldhauser, J. A. Maruhn, and C. D. Munz. "New Algorithms for Ultra-relativistic Numerical Hydrodynamics." Journal of Computational Physics 105, no. 1 (March 1993): 92–107. http://dx.doi.org/10.1006/jcph.1993.1056.

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8

Font, J. A., J. M. Marti, J. M. Ibáñez, and E. Müller. "A Numerical Study of Relativistic Jets." Symposium - International Astronomical Union 175 (1996): 435–36. http://dx.doi.org/10.1017/s0074180900081353.

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Анотація:
Numerical simulations of supersonic jets are able to explain the structures observed in many VLA images of radio sources. The improvements achieved in classical simulations (see Hardee, these proceedings) are in contrast with the almost complete lack of relativistic simulations the reason being that numerical difficulties arise from the highly relativistic flows typical of extragalactic jets. For our study, we have developed a two-dimensional code which is based on (i) an explicit conservative differencing of the special relativistic hydrodynamics (SRH) equations and (ii) the use of an approximate Riemann solver (see Martí et al. 1995a,b and references therein).
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9

Porter-Sobieraj, Joanna, Marcin Słodkowski, Daniel Kikoła, Jan Sikorski, and Paweł Aszklar. "A MUSTA-FORCE Algorithm for Solving Partial Differential Equations of Relativistic Hydrodynamics." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 1 (February 23, 2018): 25–35. http://dx.doi.org/10.1515/ijnsns-2016-0131.

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Анотація:
AbstractUnderstanding event-by-event correlations and fluctuations is crucial for the comprehension of the dynamics of heavy ion collisions. Relativistic hydrodynamics is an elegant tool for modelling these phenomena; however, such simulations are time-consuming, and conventional CPU calculations are not suitable for event-by-event calculations. This work presents a feasibility study of a new hydrodynamic code that employs graphics processing units together with a general MUSTA-FORCE algorithm (Multi-Stage Riemann Algorithm – First-Order Centred Scheme) to deliver a high-performance yet universal tool for event-by-event hydrodynamic simulations. We also investigate the performance of selected slope limiters that reduce the amount of numeric oscillations and diffusion in the presence of strong discontinuities and shock waves. The numerical results are compared to the exact solutions to assess the code’s accuracy.
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10

Sokolov, Igor V., Hui-Min Zhang, Kyoko Furusawa, and Jun-Ichi Sakai. "Artificial Wind Numerical Scheme for MHD and Relativistic Hydrodynamics." Progress of Theoretical Physics Supplement 138 (2000): 706–7. http://dx.doi.org/10.1143/ptps.138.706.

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11

Blakely, P. M., N. Nikiforakis, and W. D. Henshaw. "Assessment of the MUSTA approach for numerical relativistic hydrodynamics." Astronomy & Astrophysics 575 (March 2015): A102. http://dx.doi.org/10.1051/0004-6361/201425182.

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12

Ibáñez, José María, Isabel Cordero-Carrión, and Juan Antonio Miralles. "On numerical relativistic hydrodynamics and barotropic equations of state." Classical and Quantum Gravity 29, no. 15 (June 27, 2012): 157001. http://dx.doi.org/10.1088/0264-9381/29/15/157001.

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13

REZZOLLA, LUCIANO, and OLINDO ZANOTTI. "An improved exact Riemann solver for relativistic hydrodynamics." Journal of Fluid Mechanics 449 (December 10, 2001): 395–411. http://dx.doi.org/10.1017/s0022112001006450.

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Анотація:
A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general, when solving the Riemann problem numerically, the determination of the specific wave pattern produced is obtained through some initial guess which can be successively discarded or improved. We here discuss a new procedure, suitable for implementation in an exact Riemann solver in one dimension, which removes the initial ambiguity in the wave pattern. In particular we focus our attention on the relativistic velocity jump between the two initial states and use this to determine, through some analytic conditions, the wave pattern produced by the decay of the initial discontinuity. The exact Riemann problem is then solved by means of calculating the root of a nonlinear equation. Interestingly, in the case of two rarefaction waves, this root can even be found analytically. Our procedure is straightforward to implement numerically and improves the efficiency of numerical codes based on exact Riemann solvers.
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14

Dieselhorst, Tobias, William Cook, Sebastiano Bernuzzi, and David Radice. "Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics." Symmetry 13, no. 11 (November 11, 2021): 2157. http://dx.doi.org/10.3390/sym13112157.

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Анотація:
The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.
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15

DOS REIS, A. L. V. R., F. GRASSI, R. P. G. DE ANDRADE, Y. HAMA, and F. S. NAVARRA. "CHARGED PARTICLE RAPIDITY DISTRIBUTION, TRANSVERSE MOMENTUM DISTRIBUTION AND ELLIPTIC FLOW IN Cu+Cu COLLISIONS AT RHIC WITH NeXSPheRIO." International Journal of Modern Physics E 16, no. 09 (October 2007): 2970–73. http://dx.doi.org/10.1142/s0218301307008847.

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In this work we use the program SPheRIO1 (Smoothed Particle hydrodynamics evolution of Relativistic Ion collisions) to simulate the collision between two copper nuclei at 200 A GeV. SPheRIO is a numerical program that solves the hydrodynamics equations. We use the initial conditions provided by the program NeXus.2.
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16

Roth, Nathaniel, Peter Anninos, Peter B. Robinson, J. Luc Peterson, Brooke Polak, Tymothy K. Mangan, and Kyle Beyer. "General Relativistic Implicit Monte Carlo Radiation-hydrodynamics." Astrophysical Journal 933, no. 2 (July 1, 2022): 226. http://dx.doi.org/10.3847/1538-4357/ac75cb.

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Abstract We report on a new capability added to our general relativistic radiation-magnetohydrodynamics code, Cosmos++: an implicit Monte Carlo (IMC) treatment for radiation transport. The method is based on a Fleck-type implicit discretization of the radiation-hydrodynamics equations, but generalized for both Newtonian and relativistic regimes. A multiple reference frame approach is used to geodesically transport photon packets (and solve the hydrodynamics equations) in the coordinate frame, while radiation–matter interactions are handled either in the fluid or electron frames then communicated via Lorentz boosts and orthonormal tetrad bases attached to the fluid. We describe a method for constructing estimators of radiation moments using path-weighting that generalizes to arbitrary coordinate systems in flat or curved spacetime. Absorption, emission, scattering, and relativistic Comptonization are among the matter interactions considered in this report. We discuss our formulations and numerical methods, and validate our models against a suite of radiation and coupled radiation-hydrodynamics test problems in both flat and curved spacetimes.
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17

Martí, José Ma, and Ewald Müller. "The analytical solution of the Riemann problem in relativistic hydrodynamics." Journal of Fluid Mechanics 258 (January 10, 1994): 317–33. http://dx.doi.org/10.1017/s0022112094003344.

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Анотація:
We consider the decay of an initial discontinuity in a polytropic gas in a Minkowski space–time (the special relativistic Riemann problem). In order to get a general analytical solution for this problem, we analyse the properties of the relativistic flow across shock waves and rarefactions. As in classical hydrodynamics, the solution of the Riemann problem is found by solving an implicit algebraic equation which gives the pressure in the intermediate states. The solution presented here contains as a particular case the special relativistic shock-tube problem in which the gas is initially at rest. Finally, we discuss the impact of this result on the development of high-resolution shock-capturing numerical codes to solve the equations of relativistic hydrodynamics.
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18

Andreev, Pavel A. "Spin-electron-acoustic waves and solitons in high-density degenerate relativistic plasmas." Physics of Plasmas 29, no. 12 (December 2022): 122102. http://dx.doi.org/10.1063/5.0114914.

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Spin-electron-acoustic waves (sometimes called spin-plasmons) can be found in degenerate electron gases if spin-up electrons and spin-down electrons move relatively each other. Here, we suggest relativistic hydrodynamics with separate spin evolution, which allows us to study linear and nonlinear spin-electron-acoustic waves, including the spin-electron-acoustic solitons. The presented hydrodynamic model is the corresponding generalization of the relativistic hydrodynamic model with the average reverse gamma factor evolution, which consists of equations for evolution of the following functions: the partial concentrations (for spin-up electrons and spin-down electrons), the partial velocity fields, the partial average reverse relativistic gamma factors, and the partial flux of the reverse relativistic gamma factors. We find that the relativistic effects decrease the phase velocity of spin-electron-acoustic waves. Numerical analysis of the changes of dispersion curves of the Langmuir wave, spin-electron-acoustic wave, and ion-acoustic wave under the change of the spin polarization of electrons is presented. It is demonstrated that dispersion curves of the Langmuir wave and spin-electron-acoustic wave get closer to each other in the relativistic limit. Spin dependence of the amplitude and width of the relativistic spin-electron-acoustic soliton is demonstrated as well. Reformation of the bright soliton of potential of the electric field into the dark soliton under the influence of the relativistic effects is found.
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19

Tchekhovskoy, A., J. C. McKinney, and R. Narayan. "WHAM: a WENO-based general relativistic numerical scheme - I. Hydrodynamics." Monthly Notices of the Royal Astronomical Society 379, no. 2 (August 1, 2007): 469–97. http://dx.doi.org/10.1111/j.1365-2966.2007.11876.x.

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20

Banyuls, Francesc, Jose A. Font, Jose Ma Ibanez, Jose Ma Marti, and Juan A. Miralles. "Numerical {3 + 1} General Relativistic Hydrodynamics: A Local Characteristic Approach." Astrophysical Journal 476, no. 1 (February 10, 1997): 221–31. http://dx.doi.org/10.1086/303604.

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21

Choi, Eunwoo, and Dongsu Ryu. "Numerical relativistic hydrodynamics based on the total variation diminishing scheme." New Astronomy 11, no. 2 (November 2005): 116–29. http://dx.doi.org/10.1016/j.newast.2005.06.010.

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22

Takamoto, Makoto, and Shu-ichiro Inutsuka. "A fast numerical scheme for causal relativistic hydrodynamics with dissipation." Journal of Computational Physics 230, no. 18 (August 2011): 7002–17. http://dx.doi.org/10.1016/j.jcp.2011.05.030.

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23

MacFadyen, A. I. "Long GRBs and Supernovae from Collapsars." International Astronomical Union Colloquium 192 (2005): 417–23. http://dx.doi.org/10.1017/s0252921100009490.

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Анотація:
SummaryLong duration gamma-ray bursts are associated with the death of massive stars as earlier observations and theoretical arguments had suggested. Supernova 2003dh observed with GRB030329 confirms this picture. Current progress in developing numerical special relativistic hydrodynamics codes with adaptive mesh refinement is allowing for high-resolution simulations of relativistic flow relevant for simulations of GRBs.
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24

Chang, Philip, and Zachariah B. Etienne. "General relativistic hydrodynamics on a moving-mesh I: static space–times." Monthly Notices of the Royal Astronomical Society 496, no. 1 (June 3, 2020): 206–14. http://dx.doi.org/10.1093/mnras/staa1532.

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Анотація:
ABSTRACT We present the moving-mesh general relativistic hydrodynamics solver for static space–times as implemented in the code, MANGA. Our implementation builds on the architectures of MANGA and the numerical relativity python package NRPy+. We review the general algorithm to solve these equations and, in particular, detail the time-stepping; Riemann solution across moving faces; conversion between primitive and conservative variables; validation and correction of hydrodynamic variables; and mapping of the metric to a Voronoi moving-mesh grid. We present test results for the numerical integration of an unmagnetized Tolman–Oppenheimer–Volkoff star for 24 dynamical times. We demonstrate that at a resolution of 106 mesh generating points, the star is stable and its central density drifts downwards by 2 per cent over this time-scale. At a lower resolution, the central density drift increases in a manner consistent with the adopted second-order spatial reconstruction scheme. These results agree well with the exact solutions, and we find the error behaviour to be similar to Eulerian codes with second-order spatial reconstruction. We also demonstrate that the new code recovers the fundamental mode frequency for the same TOV star but with its initial pressure depleted by 10 per cent.
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25

Zhang, Hui-Min, Igor V. Sokolov, Kyoko Furusawa, and Jun-Ichi Sakai. "Applications of Artificial Wind Numerical Scheme for Relativistic Hydrodynamics in Astrophysics." Progress of Theoretical Physics Supplement 138 (2000): 642–43. http://dx.doi.org/10.1143/ptps.138.642.

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26

Townsend, Jamie F., László Könözsy, and Karl W. Jenkins. "On the development of a rotated-hybrid HLL/HLLC approximate Riemann solver for relativistic hydrodynamics." Monthly Notices of the Royal Astronomical Society 496, no. 2 (June 13, 2020): 2493–505. http://dx.doi.org/10.1093/mnras/staa1648.

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ABSTRACT This work presents the development of a rotated-hybrid Riemann solver for solving relativistic hydrodynamics (RHD) problems with the hybridization of the HLL and HLLC (or Rusanov and HLLC) approximate Riemann solvers. A standalone application of the HLLC Riemann solver can produce spurious numerical artefacts when it is employed in conjunction with Godunov-type high-order methods in the presence of discontinuities. It has been found that a rotated-hybrid Riemann solver with the proposed HLL/HLLC (Rusanov/HLLC) scheme could overcome the difficulty of the spurious numerical artefacts and presents a robust solution for the Carbuncle problem. The proposed rotated-hybrid Riemann solver provides sufficient numerical dissipation to capture the behaviour of strong shock waves for RHD. Therefore, in this work, we focus on two benchmark test cases (odd–even decoupling and double-Mach reflection problems) and investigate two astrophysical phenomena, the relativistic Richtmyer–Meshkov instability and the propagation of a relativistic jet. In all presented test cases, the Carbuncle problem is shown to be eliminated by employing the proposed rotated-hybrid Riemann solver. This strategy is problem-independent, straightforward to implement and provides a consistent robust numerical solution when combined with Godunov-type high-order schemes for RHD.
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27

Kulikov, Igor, Igor Chernykh, Dmitry Karavaev, Vladimir Prigarin, Anna Sapetina, Ivan Ulyanichev, and Oleg Zavyalov. "A New Parallel Code Based on a Simple Piecewise Parabolic Method for Numerical Modeling of Colliding Flows in Relativistic Hydrodynamics." Mathematics 10, no. 11 (May 30, 2022): 1865. http://dx.doi.org/10.3390/math10111865.

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Анотація:
A new parallel code based on models of special relativistic hydrodynamics is presented for describing interacting flows. A new highly accurate numerical method is considered and verified. A parallel implementation of the method by means of Coarray Fortran technology and its efficiency are described in detail. The code scalability is 92% on a cluster with Intel Xeon 6248R NKS-1P with 192 Coarray Fortran images. Different interacting relativistic flows are considered as astrophysical applications.
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28

Słodkowski, Marcin, Patryk Gawryszewski, Patryk Marcinkowski, Dominik Setniewski, and Joanna Porter-Sobieraj. "Simulations of Energy Losses in the Bulk Nuclear Medium Using Hydrodynamics on the Graphics Cards (GPU)." Proceedings 10, no. 1 (April 15, 2019): 27. http://dx.doi.org/10.3390/proceedings2019010027.

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Анотація:
We are developing a software for energy loss simulation which is affected by jets in the nuclear matter described by relativistic hydrodynamics. Our program uses a Cartesian coordinate system in order to provide high spatial resolution for the analysis of jets propagation in nuclear matter. In this work, we use 7th order WENO numerical algorithm which is resistant to numerical oscillations and diffusions. For simulating energy losses in the bulk nuclear medium, we develop efficient hydrodynamic simulation program for parallel computing using Graphics Processing Unit (GPU) and Compute Unified Device Architecture (CUDA). It allows us to prepare event-by-event simulations in high computing precision in order to study jet modifications in the medium and event-by-event simulations of fluctuating initial conditions. In our simulation, we start the hydrodynamic simulation from generation initial condition based on the UrQMD model in order to simulate comparable nucleus-nucleus interaction in the RHIC and LHC energies. The main part of this simulation is the computation of hydrodynamic system evolution. We present obtained energy density distributions which can be compared to experimental results.
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29

HAIN, S., P. MULSER, F. CORNOLTI, and H. OPOWER. "Hydrodynamic models and schemes for fast ignition." Laser and Particle Beams 17, no. 2 (April 1999): 245–63. http://dx.doi.org/10.1017/s0263034699172100.

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In this paper, we want to discuss different hydrodynamic schemes for fast ignition and some of their basic effects. Relativistic hydrodynamics and a covariant generalized Ohm's law are presented. Matter perforation (hole boring) by an intense laser pulse is investigated by 2D numerical simulations and a simple formula for the perforation speed is derived. Furthermore, we study macroparticle acceleration by an intense laser beam and the possibility to provide an energetic and massive projectile for ballistic ignition. The dynamics of ignition of a precompressed D–T mixture is illustrated by numerical simulations in planar 2D geometry using direct laser irradiation and macroparticle impact as external drivers. Electron heat conduction is found to be responsible for an efficient burn wave propagation which prevents the hot gas bubble of burning fuel from deflagrating into vacuum.
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30

Maldonado-Gonzalez, Julio Cesar, Alejandro Ayala, Isabel Dominguez, and Maria Elena Tejeda-Yeomans. "QGP hydrodynamical study using energy-momentum in-medium deposition by an extended source." EPJ Web of Conferences 172 (2018): 08003. http://dx.doi.org/10.1051/epjconf/201817208003.

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Анотація:
The quark-gluon plasma (QGP) is created under extreme conditions, such as the ones prevailing in heavy ion collisions. The characterization of the QGP can be done using high-pT probes such as the partons that are created through hard scatterings in the fireball. These fast-moving partons lose energy and momentum along their traveled path through the medium. The parton deposition of energy-momentum creates an in-medium disturbance that can be described using approximations within relativistic hydrodynamics in a defined regime of the QGP evolution. Based on earlier research in this field, we study the use of extended sources that depend on the location of the parton-jet in the initial stages of the QGP evolution. We explore this approach as a way to complement the current numerical landscape of hydrodynamical QGP studies and to eventually generate initial conditions that can be used as input of hydrodynamical numerical simulations.
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31

Musoke, G., A. J. Young, and M. Birkinshaw. "Hydrodynamic simulations of AGN jets: the impact of Riemann solvers and spatial reconstruction schemes on jet evolution." Monthly Notices of the Royal Astronomical Society 498, no. 3 (September 2, 2020): 3870–87. http://dx.doi.org/10.1093/mnras/staa2657.

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ABSTRACT Numerical simulations play an essential role in helping us to understand the physical processes behind relativistic jets in active galactic nuclei. The large number of hydrodynamic codes available today enables a variety of different numerical algorithms to be utilized when conducting the simulations. Since many of the simulations presented in the literature use different combinations of algorithms it is important to quantify the differences in jet evolution that can arise due to the precise numerical schemes used. We conduct a series of simulations using the flash (magneto-)hydrodynamics code in which we vary the Riemann solver and spatial reconstruction schemes to determine their impact on the evolution and dynamics of the jets. For highly refined grids the variation in the simulation results introduced by the different combinations of spatial reconstruction scheme and Riemann solver is typically small. A high level of convergence is found for simulations using third-order spatial reconstruction with the Harten–Lax–Van-Leer with contact and Hybrid Riemann solvers.
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32

He, Peng, and Huazhong Tang. "An Adaptive Moving Mesh Method for Two-Dimensional Relativistic Hydrodynamics." Communications in Computational Physics 11, no. 1 (January 2012): 114–46. http://dx.doi.org/10.4208/cicp.291010.180311a.

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AbstractThis paper extends the adaptive moving mesh method developed by Tang and Tang [36] to two-dimensional (2D) relativistic hydrodynamic (RHD) equations. The algorithm consists of two “independent” parts: the time evolution of the RHD equations and the (static) mesh iteration redistribution. In the first part, the RHD equations are discretized by using a high resolution finite volume scheme on the fixed but nonuniform meshes without the full characteristic decomposition of the governing equations. The second part is an iterative procedure. In each iteration, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed method.
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33

Zhao, Jian, and Huazhong Tang. "Runge-Kutta Central Discontinuous Galerkin Methods for the Special Relativistic Hydrodynamics." Communications in Computational Physics 22, no. 3 (July 6, 2017): 643–82. http://dx.doi.org/10.4208/cicp.oa-2016-0192.

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Анотація:
AbstractThis paper develops Runge-Kutta PK-based central discontinuous Galerkin (CDG) methods with WENO limiter for the one- and two-dimensional special relativistic hydrodynamical (RHD) equations, K = 1,2,3. Different from the non-central DG methods, the Runge-Kutta CDG methods have to find two approximate solutions defined on mutually dual meshes. For each mesh, the CDG approximate solutions on its dual mesh are used to calculate the flux values in the cell and on the cell boundary so that the approximate solutions on mutually dual meshes are coupled with each other, and the use of numerical flux will be avoided. The WENO limiter is adaptively implemented via two steps: the “troubled” cells are first identified by using a modified TVB minmod function, and then the WENO technique is used to locally reconstruct new polynomials of degree (2K+1) replacing the CDG solutions inside the “troubled” cells by the cell average values of the CDG solutions in the neighboring cells as well as the original cell averages of the “troubled” cells. Because the WENO limiter is only employed for finite “troubled” cells, the computational cost can be as little as possible. The accuracy of the CDG without the numerical dissipation is analyzed and calculation of the flux integrals over the cells is also addressed. Several test problems in one and two dimensions are solved by using our Runge-Kutta CDG methods with WENO limiter. The computations demonstrate that our methods are stable, accurate, and robust in solving complex RHD problems.
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34

QAMAR, SHAMSUL, and GERALD WARNECKE. "A HIGH ORDER KINETIC FLUX-SPLITTING METHOD FOR THE SPECIAL RELATIVISTIC HYDRODYNAMICS." International Journal of Computational Methods 02, no. 01 (March 2005): 49–74. http://dx.doi.org/10.1142/s0219876205000338.

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In this article we present a flux splitting method based on gas-kinetic theory for the special relativistic hydrodynamics (SRHD) [Landau and Lifshitz, Fluid Mechanics, Pergamon New York, 1987] in one and two space dimensions. This kinetic method is based on the direct splitting of the macroscopic flux functions with the consideration of particle transport. At the same time, particle "collisions" are implemented in the free transport process to reduce numerical dissipation. Due to the nonlinear relations between conservative and primitive variables and the consequent complexity of the Jacobian matrix, the multi-dimensional shock-capturing numerical schemes for SRHD are computationally more expensive. All the previous methods presented for the solution of these equations were based on the macroscopic continuum description. These upwind high-resolution shock-capturing (HRSC) schemes, which were originally made for non-relativistic flows, were extended to SRHD. However our method, which is based on kinetic theory is more related to the physics of these equations and is very efficient, robust, and easy to implement. In order to get high order accuracy in space, we use a third order central weighted essentially non-oscillatory (CWENO) finite difference interpolation routine. To achieve high order accuracy in time we use a Runge-Kutta time stepping method. The one- and two-dimensional computations reported in this paper show the desired accuracy, high resolution, and robustness of the method.
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35

Falle, S. A. E. G., and S. S. Komissarov. "An upwind numerical scheme for relativistic hydrodynamics with a general equation of state." Monthly Notices of the Royal Astronomical Society 278, no. 2 (January 11, 1996): 586–602. http://dx.doi.org/10.1093/mnras/278.2.586.

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36

Dubus, G., A. Lamberts, and S. Fromang. "Modelling the high-energy emission from gamma-ray binaries using numerical relativistic hydrodynamics." Astronomy & Astrophysics 581 (August 27, 2015): A27. http://dx.doi.org/10.1051/0004-6361/201425394.

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37

Słodkowski, Marcin, Dominik Setniewski, Paweł Aszklar, and Joanna Porter-Sobieraj. "Modeling the Dynamics of Heavy-Ion Collisions with a Hydrodynamic Model Using a Graphics Processor." Symmetry 13, no. 3 (March 20, 2021): 507. http://dx.doi.org/10.3390/sym13030507.

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Dense bulk matter is formed during heavy-ion collision and expands towards a vacuum. It behaves as a perfect fluid, described by relativistic hydrodynamics. In order to study initial condition fluctuation and properties of jet propagation in dense hot matter, we assume a Cartesian laboratory frame with several million cells in a stencil with high-accuracy data volume grids. Employing numerical algorithms to solve hydrodynamic equations in such an assumption requires a lot of computing power. Hydrodynamic simulations of nucleus + nucleus interactions in the range of energies of the Large Hadron Collider (LHC) are carried out using our program, which uses Graphics Processing Units (GPUs) and Compute Unified Device Architecture (CUDA). In this work, we focused on transforming hydrodynamic quantities into kinetic descriptions. We implemented the hypersurface freeze-out conditions using marching cubes techniques. We developed freeze-out procedures to obtain the momentum distributions of particles on the hypersurface. The final particle distributions, elliptic flow, and higher harmonics are comparable to the experimental LHC data.
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38

Fromm, C. M., Z. Younsi, A. Baczko, Y. Mizuno, O. Porth, M. Perucho, H. Olivares, et al. "Using evolutionary algorithms to model relativistic jets." Astronomy & Astrophysics 629 (August 22, 2019): A4. http://dx.doi.org/10.1051/0004-6361/201834724.

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Context. High-resolution very long baseline interferometry (VLBI) observations of NGC 1052 show a two sided jet with several regions of enhanced emission and a clear emission gap between the two jets. This gap shrinks with increasing frequency and vanishes around ν ∼ 43 GHz. The observed structures are due to both the macroscopic fluid dynamics interacting with the surrounding ambient medium including an obscuring torus and the radiation microphysics. In order to model the observations of NGC 1052 via state-of-the art numerical simulations both the fluid-dynamical and emission processes have to be taken into account. Aims. In this paper we investigate the possible physical conditions in relativistic jets of NGC 1052 by directly modelling the observed emission and spectra via state-of-the-art special-relativistic hydrodynamic (SRHD) simulations and radiative transfer calculations. Methods. We performed SRHD simulations of over-pressured and pressure-matched jets using the special-relativistic hydrodynamics code Ratpenat. To investigate the physical conditions in the relativistic jet we coupled our radiative transfer code to evolutionary algorithms and performed simultaneous modelling of the observed jet structure and the broadband radio spectrum. During the calculation of the radiation we consider non-thermal emission from the jet and thermal absorption in the obscuring torus. In order to compare our model to VLBI observations we take into account the sparse sampling of the u-v plane, the array properties and the imaging algorithm. Results. We present for the first time an end-to-end pipeline for fitting numerical simulations to VLBI observations of relativistic jets taking into account the macro-physics including fluid dynamics and ambient medium configurations together with thermal and non-thermal emission and the properties of the observing array. The detailed analysis of our simulations shows that the structure and properties of the observed relativistic jets in NGC 1052 can be reconstructed by a slightly over-pressured jet (dk ∼ 1.5) embedded in a decreasing pressure ambient medium
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39

Akimova, Elena N., Vladimir E. Misilov, Igor M. Kulikov, and Igor G. Chernykh. "OMPEGAS: Optimized Relativistic Code for Multicore Architecture." Mathematics 10, no. 14 (July 21, 2022): 2546. http://dx.doi.org/10.3390/math10142546.

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The paper presents a new hydrodynamical code, OMPEGAS, for the 3D simulation of astrophysical flows on shared memory architectures. It provides a numerical method for solving the three-dimensional equations of the gravitational hydrodynamics based on Godunov’s method for solving the Riemann problem and the piecewise parabolic approximation with a local stencil. It obtains a high order of accuracy and low dissipation of the solution. The code is implemented for multicore processors with vector instructions using the OpenMP technology, Intel SDLT library, and compiler auto-vectorization tools. The model problem of simulating a star explosion was used to study the developed code. The experiments show that the presented code reproduces the behavior of the explosion correctly. Experiments for the model problem with a grid size of 128×128×128 were performed on an 16-core Intel Core i9-12900K CPU to study the efficiency and performance of the developed code. By using the autovectorization, we achieved a 3.3-fold increase in speed in comparison with the non-vectorized program on the processor with AVX2 support. By using multithreading with OpenMP, we achieved an increase in speed of 2.6 times on a 16-core processor in comparison with the vectorized single-threaded program. The total increase in speed was up to ninefold.
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40

Wu, Kailiang, Zhicheng Yang, and Huazhong Tang. "A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics." East Asian Journal on Applied Mathematics 4, no. 2 (May 2014): 95–131. http://dx.doi.org/10.4208/eajam.101013.100314a.

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AbstractA third-order accurate direct Eulerian generalised Riemann problem (GRP) scheme is derived for the one-dimensional special relativistic hydrodynamical equations. In our GRP scheme, the higher-order WENO initial reconstruction is employed, and the local GRPs in the Eulerian formulation are directly and analytically resolved to third-order accuracy via the Riemann invariants and Rankine-Hugoniot jump conditions, to get the approximate states in numerical fluxes. Unlike a previous second-order accurate GRP scheme, for the non-sonic case the limiting values of the second-order time derivatives of the fluid variables at the singular point are also needed for the calculation of the approximate states; while for the sonic case, special attention is paid because the calculation of the second-order time derivatives at the sonic point is difficult. Several numerical examples are given to demonstrate the accuracy and effectiveness of our GRP scheme.
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41

Sotani, Hajime, and Kohsuke Sumiyoshi. "Stability of the protoneutron stars towards black hole formation." Monthly Notices of the Royal Astronomical Society 507, no. 2 (August 10, 2021): 2766–76. http://dx.doi.org/10.1093/mnras/stab2301.

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ABSTRACT We examine the protoneutron star (PNS) stability in this study by solving the radial oscillation equations. For this purpose, we adopt the numerical results of a massive PNS towards the black hole formation obtained by spherically symmetric numerical simulations for a core-collapse supernova with general relativistic neutrino-radiation hydrodynamics. We find that the PNSs are basically stable in their evolution against the radial perturbations, while the PNS finally becomes unstable before the apparent horizon appears inside the PNS. We also examine the gravitational wave frequencies from the PNS with the relativistic Cowling approximation. Then, we derive the empirical formula for the f-mode frequency, which weakly depends on the PNS models. This kind of universality tells us the PNS property, which is a combination of the PNS mass and radius in this study, once one would observe the f-mode gravitational waves.
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42

Wu, Zhenyu, Giacomo Ricigliano, Rahul Kashyap, Albino Perego, and David Radice. "Radiation hydrodynamics modelling of kilonovae with SNEC." Monthly Notices of the Royal Astronomical Society 512, no. 1 (February 15, 2022): 328–47. http://dx.doi.org/10.1093/mnras/stac399.

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ABSTRACT We develop a method to compute synthetic kilonova light curves that combine numerical relativity simulations of neutron star mergers and the SNEC radiation–hydrodynamics code. We describe our implementation of initial and boundary conditions, r-process heating, and opacities for kilonova simulations. We validate our approach by carefully checking that energy conservation is satisfied and by comparing the SNEC results with those of two semi-analytic light-curve models. We apply our code to the calculation of colour light curves for three binaries having different mass ratios (equal and unequal mass) and different merger outcome (short-lived and long-lived remnants). We study the sensitivity of our results to hydrodynamic effects, nuclear physics uncertainties in the heating rates, and duration of the merger simulations. We find that hydrodynamics effects are typically negligible and that homologous expansion is a good approximation in most cases. However, pressure forces can amplify the impact of uncertainties in the radioactive heating rates. We also study the impact of shocks possibly launched into the outflows by a relativistic jet. None of our models match AT2017gfo, the kilonova in GW170817. This points to possible deficiencies in our merger simulations and kilonova models that neglect non-LTE effects and possible additional energy injection from the merger remnant and to the need to go beyond the assumption of spherical symmetry adopted in this work.
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43

ALBERICO, W. M., A. BERAUDO, A. DE PACE, A. MOLINARI, M. MONTENO, M. NARDI, and F. PRINO. "LANGEVIN DYNAMICS OF HEAVY FLAVORS IN RELATIVISTIC HEAVY-ION COLLISIONS." International Journal of Modern Physics E 20, no. 07 (July 2011): 1623–28. http://dx.doi.org/10.1142/s0218301311019982.

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We study the stochastic dynamics of c and b quarks, produced in hard initial processes, in the hot medium created after the collision of two relativistic heavy ions. This is done through the numerical solution of the relativistic Langevin equation. The latter requires the knowledge of the friction and diffusion coefficients, whose microscopic evaluation is performed treating separately the contribution of soft and hard collisions. The evolution of the background medium is described by ideal/viscous hydrodynamics. Below the critical temperature the heavy quarks are converted into hadrons, whose semileptonic decays provide single-electron spectra to be compared with the current experimental data measured at RHIC. We focus on the nuclear modification factor RAA and on the elliptic-flow coefficient v2, getting, for sufficiently large pT, a reasonable agreement.
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44

Kedia, Atul, Grant Mathews, Hee Il Kim, and In-Saeng Suh. "Binary neutron star mergers of quark matter based nuclear equations of state." EPJ Web of Conferences 260 (2022): 11004. http://dx.doi.org/10.1051/epjconf/202226011004.

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With observations of gravitational wave signals from binary neutron star mergers (BNSM) by LIGO-Virgo-KAGRA (LVK) Collaboration and NICER, the nuclear equation of state (EOS) is becoming increasingly testable by complementary numerical simulations. Numerous simulations currently explore the EOS at different density regimes for the constituent neutron stars specifically narrowing the uncertainty in the sub-nuclear densities. In this paper we summarize the three-dimensional general relativistic-hydrodynamics based simulations of BNSMs for EOSs with a specific emphasis on the quark matter EOS at the highest densities.
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45

Kulikov, Igor, Igor Chernykh, Anna Sapetina, and Vladimir Prigarin. "A new MPI/OpenMP code for numerical modeling of relativistic hydrodynamics by means adaptive nested meshes." Journal of Physics: Conference Series 1336 (November 2019): 012008. http://dx.doi.org/10.1088/1742-6596/1336/1/012008.

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46

Wu, Kailiang. "Minimum Principle on Specific Entropy and High-Order Accurate Invariant-Region-Preserving Numerical Methods for Relativistic Hydrodynamics." SIAM Journal on Scientific Computing 43, no. 6 (January 2021): B1164—B1197. http://dx.doi.org/10.1137/21m1397994.

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47

Cannizzo, John K., Neil Gehrels, and Ethan T. Vishniac. "A Numerical Gamma‐Ray Burst Simulation Using Three‐Dimensional Relativistic Hydrodynamics: The Transition from Spherical to Jetlike Expansion." Astrophysical Journal 601, no. 1 (January 20, 2004): 380–90. http://dx.doi.org/10.1086/380436.

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48

Dönmez, Orhan. "Solving 1-D special relativistic hydrodynamics (SRH) equations using different numerical methods and results from different test problems." Applied Mathematics and Computation 181, no. 1 (October 2006): 256–70. http://dx.doi.org/10.1016/j.amc.2006.01.031.

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49

Weih, Lukas R., Hector Olivares, and Luciano Rezzolla. "Two-moment scheme for general-relativistic radiation hydrodynamics: a systematic description and new applications." Monthly Notices of the Royal Astronomical Society 495, no. 2 (May 11, 2020): 2285–304. http://dx.doi.org/10.1093/mnras/staa1297.

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ABSTRACT We provide a systematic description of the steps necessary – and of the potential pitfalls to be encountered – when implementing a two-moment scheme within an implicit–explicit (IMEX) scheme to include radiative-transfer contributions in numerical simulations of general-relativistic (magneto-)hydrodynamics (GRMHD). We make use of the M1 closure, which provides an exact solution for the optically thin and thick limits, and an interpolation between these limits. Special attention is paid to the efficient solution of the emerging set of implicit conservation equations. In particular, we present an efficient method for solving these equations via the inversion of a 4 × 4-matrix within an IMEX scheme. While this method relies on a few approximations, it offers a very good compromise between accuracy and computational efficiency. After a large number of tests in special relativity, we couple our new radiation code, frac, with the GRMHD code bhac to investigate the radiative Michel solution, namely, the problem of spherical accretion on to a black hole in the presence of a radiative field. By performing the most extensive exploration of the parameter space for this problem, we find that the accretion’s efficiency can be expressed in terms of physical quantities such as temperature, T, luminosity, L, and black hole mass, M, via the expression $\varepsilon =(L/L_{\rm Edd})/(\dot{M}/\dot{M}_{\rm Edd})= 7.41\times 10^{-7}\left(T/10^6\, \mathrm{K}\right)^{0.22} \left(L/L_\odot \right)^{0.48} \left(M/M_\odot \right)^{0.48}$, where LEdd and $\dot{M}_{\mathrm{Edd}}$ are the Eddington luminosity and accretion rate, respectively. Finally, we also consider the accretion problem away from spherical symmetry, finding that the solution is stable under perturbations in the radiation field.
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50

Meliani, Zakaria, Yosuke Mizuno, Hector Olivares, Oliver Porth, Luciano Rezzolla, and Ziri Younsi. "Simulations of recoiling black holes: adaptive mesh refinement and radiative transfer." Astronomy & Astrophysics 598 (January 27, 2017): A38. http://dx.doi.org/10.1051/0004-6361/201629191.

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Context. In many astrophysical phenomena, and especially in those that involve the high-energy regimes that always accompany the astronomical phenomenology of black holes and neutron stars, physical conditions that are achieved are extreme in terms of speeds, temperatures, and gravitational fields. In such relativistic regimes, numerical calculations are the only tool to accurately model the dynamics of the flows and the transport of radiation in the accreting matter. Aims. We here continue our effort of modelling the behaviour of matter when it orbits or is accreted onto a generic black hole by developing a new numerical code that employs advanced techniques geared towards solving the equations of general-relativistic hydrodynamics. Methods. More specifically, the new code employs a number of high-resolution shock-capturing Riemann solvers and reconstruction algorithms, exploiting the enhanced accuracy and the reduced computational cost of adaptive mesh-refinement (AMR) techniques. In addition, the code makes use of sophisticated ray-tracing libraries that, coupled with general-relativistic radiation-transfer calculations, allow us to accurately compute the electromagnetic emissions from such accretion flows. Results. We validate the new code by presenting an extensive series of stationary accretion flows either in spherical or axial symmetry that are performed either in two or three spatial dimensions. In addition, we consider the highly nonlinear scenario of a recoiling black hole produced in the merger of a supermassive black-hole binary interacting with the surrounding circumbinary disc. In this way, we can present for the first time ray-traced images of the shocked fluid and the light curve resulting from consistent general-relativistic radiation-transport calculations from this process. Conclusions. The work presented here lays the ground for the development of a generic computational infrastructure employing AMR techniques to accurately and self-consistently calculate general-relativistic accretion flows onto compact objects. In addition to the accurate handling of the matter, we provide a self-consistent electromagnetic emission from these scenarios by solving the associated radiative-transfer problem. While magnetic fields are currently excluded from our analysis, the tools presented here can have a number of applications to study accretion flows onto black holes or neutron stars.
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