This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.Electronic Supplementary MaterialSupplementary material is available for this article at 10.12942/lrr-2003-7 and is accessible for authorized users.

The main features of a three dimensional, high-resolution special relativistic hydro code based on relativistic Riemann solvers are described. The capabilities and performance of the code are discussed. In particular, we present the results of extensive test calculations which demonstrate that the code can accurately and efficiently handle strong shocks in three spatial dimensions. Results of the performance of the code on single and multi-processor machines are given. Simulations (in double precision) with ≤ 7 10 6 computational cells require less than 1 Gb of RAM memory and ≈ 7 10 −5 CPU seconds per zone and time step (on a SCI Cray-Origin 2000 with a R10000 processor). Currently, a version of the numerical code is under development, which is suited for massively parallel computers with distributed memory architecture (like, e.g., Cray T3E).

We study the influence of the matter content of extragalactic jets on their morphology, dynamics and emission properties. For this purpose we consider jets of extremely different compositions, including pure leptonic and baryonic plasmas. Our work is based on two‐dimensional relativistic hydrodynamic simulations of the long‐term evolution of powerful extragalactic jets propagating into a homogeneous environment. The equation of state used in the simulations accounts for an arbitrary mixture of electrons, protons and electron–positron pairs. Using the hydrodynamic models, we have also computed synthetic radio maps and the thermal bremsstrahlung X‐ray emission from their cavities. Although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets, we find that both the morphology and the dynamic behaviour are almost independent of the assumed composition of the jets. Their evolution proceeds in two distinct epochs. During the first one, multidimensional effects are unimportant and the jets propagate ballistically. The second epoch starts when the first larger vortices are produced near the jet head, causing the beam cross‐section to increase and the jet to decelerate. The evolution of the cocoon and cavity is in agreement with a simple theoretical model. The beam velocities are relativistic (Γ≃4) at kiloparsec scales, supporting the idea that the X‐ray emission of several extragalactic jets may be due to relativistically boosted CMB photons. The radio emission of all models is dominated by the contribution of the hotspots. All models exhibit a depression in the X‐rays surface brightness of the cavity interior, in agreement with recent observations.

This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results obtained with different numerical SRHD methods are compared, and two astrophysical applications of SRHD flows are discussed. An evaluation of the various numerical methods is given and future developments are analyzed.Electronic Supplementary MaterialSupplementary material is available for this article at 10.12942/lrr-1999-3.

Abstract.We assess the suitability of a recent high-resolution central scheme developed by Kurganov & Tadmor (2000) for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime.Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates. Article RevisionsLiving Reviews supports two ways of keeping its articles up-to-date:Fast-track revision. A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here.Major update. A major update will include substantial changes and additions and is subject to full external refereeing. It is published with a new publication number.For detailed documentation of an article's evolution, please refer to the history document of the article's online version at http://dx

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We present a model to determine the physical parameters of jets and hot spots of a sample of compact symmetric objects (CSOs) under very basic assumptions like synchrotron emission and minimum energy conditions. Based on this model, we propose a simple evolutionary scenario for these sources assuming that they evolve in ram pressure equilibrium with the external medium and constant jet power. The parameters of our model are constrained from fits of observational data (radio luminosity, hot spot radius, and hot spot advance speed) versus projected linear size. From these plots we conclude that CSOs evolve self-similarly and that their radio luminosity increases with linear size along the first kiloparsec. Assuming that the jets feeding CSOs are relativistic from both kinematical and thermodynamical points of view, we use the values of the pressure and particle number density within the hot spots to estimate the fluxes of momentum (thrust), energy, and particles of these relativistic jets. The mean jet power obtained in this way is within an order of magnitude of that inferred for Fanaroff-Riley type 2 sources, which is consistent with CSOs being the possible precursors of large doubles. The inferred flux of particles corresponds to, for a barionic jet, about 10% of the mass accreted by a black hole of 10 8 M at the Eddington limit, pointing toward a very efficient conversion of accretion flow into ejection or to a leptonic composition of jets. We have considered three different models (namely, models I, IIa, and IIb). Model I, assuming constant hot spot advance speed and increasing luminosity, can be ruled out on the grounds of its energy cost. However, models IIa and IIb seem to describe limiting behaviors of sources evolving at constant advance speed and decreasing luminosity (model IIa) and decreasing hot spot advance speed and increasing luminosity (model IIb). In all our models the slopes of the hot spot luminosity and advance speed with source linear size are governed by only one parameter, namely, the external density gradient. A short discussion on the validity of models IIa and IIb to describe the complete evolution of powerful radio sources from their CSO phase is also included.