1,463 research outputs found
Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement
Astrophysical relativistic flow problems require high resolution
three-dimensional numerical simulations. In this paper, we describe a new
parallel three-dimensional code for simulations of special relativistic
hydrodynamics (SRHD) using both spatially and temporally structured adaptive
mesh refinement (AMR). We used the method of lines to discretize the SRHD
equations spatially and a total variation diminishing (TVD) Runge-Kutta scheme
for time integration. For spatial reconstruction, we have implemented piecewise
linear method (PLM), piecewise parabolic method (PPM), third order convex
essentially non-oscillatory (CENO) and third and fifth order weighted
essentially non-oscillatory (WENO) schemes. Flux is computed using either
direct flux reconstruction or approximate Riemann solvers including HLL,
modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR
part of the code is built on top of the cosmological Eulerian AMR code {\sl
enzo}. We discuss the coupling of the AMR framework with the relativistic
solvers. Via various test problems, we emphasize the importance of resolution
studies in relativistic flow simulations because extremely high resolution is
required especially when shear flows are present in the problem. We also
present the results of two 3d simulations of astrophysical jets: AGN jets and
GRB jets. Resolution study of those two cases further highlights the need of
high resolutions to calculate accurately relativistic flow problems.Comment: 14 pages, 23 figures. A section on 3D GRB jet simulation added.
Accepted by ApJ
A Multidimensional Relativistic Hydrodynamics Code with a General Equation of State
The ideal gas equation of state with a constant adiabatic index, although
commonly used in relativistic hydrodynamics, is a poor approximation for most
relativistic astrophysical flows. Here we propose a new general equation of
state for a multi-component relativistic gas which is consistent with the Synge
equation of state for a relativistic perfect gas and is suitable for numerical
(special) relativistic hydrodynamics. We also present a multidimensional
relativistic hydrodynamics code incorporating the proposed general equation of
state, based on the HLL scheme, which does not make use of a full
characteristic decomposition of the relativistic hydrodynamic equations. The
accuracy and robustness of this code is demonstrated in multidimensional
calculations through several highly relativistic test problems taking into
account nonvanishing tangential velocities. Results from three-dimensional
simulations of relativistic jets show that the morphology and dynamics of the
relativistic jets are significantly influenced by the different equation of
state and by different compositions of relativistic perfect gases. Our new
numerical code, combined with our proposed equation of state is very efficient
and robust, and unlike previous codes, it gives very accurate results for
thermodynamic variables in relativistic astrophysical flows.Comment: 32 pages, 9 figures, accepted by ApJ
Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations
We assess the suitability of a recent high-resolution central scheme
developed by Kurganov & Tadmor (2000) for the solution of the relativistic
hydrodynamics 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 to yield 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 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 the
exact solution of the Riemann problem is prohibitively expensive to compute
numerically. 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.Comment: 14 pages, 12 figures, to appear in A&
RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code
We have developed a new computer code, RAM, to solve the conservative
equations of special relativistic hydrodynamics (SRHD) using adaptive mesh
refinement (AMR) on parallel computers. We have implemented a
characteristic-wise, finite difference, weighted essentially non-oscillatory
(WENO) scheme using the full characteristic decomposition of the SRHD equations
to achieve fifth-order accuracy in space. For time integration we use the
method of lines with a third-order total variation diminishing (TVD)
Runge-Kutta scheme. We have also implemented fourth and fifth order Runge-Kutta
time integration schemes for comparison. The implementation of AMR and
parallelization is based on the FLASH code. RAM is modular and includes the
capability to easily swap hydrodynamics solvers, reconstruction methods and
physics modules. In addition to WENO we have implemented a finite volume module
with the piecewise parabolic method (PPM) for reconstruction and the modified
Marquina approximate Riemann solver to work with TVD Runge-Kutta time
integration. We examine the difficulty of accurately simulating shear flows in
numerical relativistic hydrodynamics codes. We show that under-resolved
simulations of simple test problems with transverse velocity components produce
incorrect results and demonstrate the ability of RAM to correctly solve these
problems. RAM has been tested in one, two and three dimensions and in
Cartesian, cylindrical and spherical coordinates. We have demonstrated
fifth-order accuracy for WENO in one and two dimensions and performed detailed
comparison with other schemes for which we show significantly lower convergence
rates. Extensive testing is presented demonstrating the ability of RAM to
address challenging open questions in relativistic astrophysics.Comment: ApJS in press, 21 pages including 18 figures (6 color figures
A multidimensional grid-adaptive relativistic magnetofluid code
A robust second order, shock-capturing numerical scheme for multi-dimensional
special relativistic magnetohydrodynamics on computational domains with
adaptive mesh refinement is presented. The base solver is a total variation
diminishing Lax-Friedrichs scheme in a finite volume setting and is combined
with a diffusive approach for controlling magnetic monopole errors. The
consistency between the primitive and conservative variables is ensured at all
limited reconstructions and the spatial part of the four velocity is used as a
primitive variable. Demonstrative relativistic examples are shown to validate
the implementation. We recover known exact solutions to relativistic MHD
Riemann problems, and simulate the shock-dominated long term evolution of
Lorentz factor 7 vortical flows distorting magnetic island chains.Comment: accepted for publication in Computer Physics Communication
AMRVAC and Relativistic Hydrodynamic simulations for GRB afterglow phases
We apply a novel adaptive mesh refinement code, AMRVAC, to numerically
investigate the various evolutionary phases in the interaction of a
relativistic shell with its surrounding cold Interstellar Medium (ISM). We do
this for both 1D isotropic as well as full 2D jetlike fireball models. This is
relevant for Gamma Ray Bursts, and we demonstrate that, thanks to the AMR
strategy, we resolve the internal structure of the shocked shell-ISM matter,
which will leave its imprint on the GRB afterglow. We determine the
deceleration from an initial Lorentz factor up to the almost
Newtonian phase of the flow. We present axisymmetric 2D
shell evolutions, with the 2D extent characterized by their initial opening
angle. In such jetlike GRB models, we discuss the differences with the 1D
isotropic GRB equivalents. These are mainly due to thermally induced sideways
expansions of both the shocked shell and shocked ISM regions. We found that the
propagating 2D ultrarelativistic shell does not accrete all the surrounding
medium located within its initial opening angle. Part of this ISM matter gets
pushed away laterally and forms a wide bow-shock configuration with swirling
flow patterns trailing the thin shell. The resulting shell deceleration is
quite different from that found in isotropic GRB models. As long as the lateral
shell expansion is merely due to ballistic spreading of the shell, isotropic
and 2D models agree perfectly. As thermally induced expansions eventually lead
to significantly higher lateral speeds, the 2D shell interacts with comparably
more ISM matter and decelerates earlier than its isotropic counterpart.Comment: 12 pages, accepted in MNRAS, 12/01/200
Dynamical Evolution of an Ultra-relativistic Fireball Colliding with a Freely Expanding Gas
We investigate the hydrodynamical evolution of an ultra-relativistic fireball
colliding with a freely expanding gas. The hydrodynamical interaction of the
fireball and the gas results in the formation of a geometrically thin shell. We
study the dynamical evolution of the shell by an analytical way and perform a
numerical simulation equipped with an adaptive mesh refinement to investigate
the internal structure of the shell. The shocked gas can give rise to bright
emission in the X-ray and gamma-ray energy range. We propose that the breakout
emission from the forward shock and the photospheric emission from the
reverse-shocked fireball contribute to early gamma-ray emission from gamma-ray
bursts.Comment: 15 pages, 9 figures, accepted for publication in Ap
Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations
This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook)
schemes in the framework of finite volume method for the ultra-relativistic
flows. Different from the existing kinetic flux-vector splitting (KFVS) or
BGK-type schemes for the ultra-relativistic Euler equations, the present
genuine BGK schemes are derived from the analytical solution of the
Anderson-Witting model, which is given for the first time and includes the
"genuine" particle collisions in the gas transport process. The BGK schemes for
the ultra-relativistic viscous flows are also developed and two examples of
ultra-relativistic viscous flow are designed. Several 1D and 2D numerical
experiments are conducted to demonstrate that the proposed BGK schemes not only
are accurate and stable in simulating ultra-relativistic inviscid and viscous
flows, but also have higher resolution at the contact discontinuity than the
KFVS or BGK-type schemes.Comment: 41 pages, 13 figure
WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics
The accurate modelling of astrophysical scenarios involving compact objects
and magnetic fields, such as the collapse of rotating magnetized stars to black
holes or the phenomenology of gamma-ray bursts, requires the solution of the
Einstein equations together with those of general-relativistic
magnetohydrodynamics. We present a new numerical code developed to solve the
full set of general-relativistic magnetohydrodynamics equations in a dynamical
and arbitrary spacetime with high-resolution shock-capturing techniques on
domains with adaptive mesh refinements. After a discussion of the equations
solved and of the techniques employed, we present a series of testbeds carried
out to validate the code and assess its accuracy. Such tests range from the
solution of relativistic Riemann problems in flat spacetime, over to the
stationary accretion onto a Schwarzschild black hole and up to the evolution of
oscillating magnetized stars in equilibrium and constructed as consistent
solutions of the coupled Einstein-Maxwell equations.Comment: minor changes to match the published versio
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