Adaptive mesh fluid simulations on GPU

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA’s CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge–Kutta time integration scheme, piecewise linear reconstruction, and a Harten–Lax–van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.     

A New Formulation for General Relativistic Force-Free Electrodynamics and Its Applications

We formulate the general relativistic force-free electrodynamics in a new 3 1 language. In this formulation,when we have properly defined electric and magnetic fields,the covariant Maxwell equations could be cast in the traditional form with new vacuum con-stitutive constraint equations. The fundamental equation governing a stationary,axisymmet-ric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3 1 system of Thorne and MacDonald,the new system of 3 1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applica-tions in flat spacetime. We investigate its application to disk wind,black hole magnetosphere and solar physics in both flat and curved spacetime.     

Explosion of a Minimum-Mass Neutron Star within Relativistic Hydrodynamics

Astronomy Letters - The relativistic hydrodynamics equations are adapted for the spherically symmetric case and the Lagrangian form. They are used to model the explosive disruption of a...     

Hyperbolic character of the angular moment equations of radiative transfer and numerical methods

We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and causality preservation lead to mathematical conditions allowing us to establish a useful characterization of the closure relations. We apply numerical methods specifically designed to solve hyperbolic systems of conservation laws (the so-called Godunov-type methods) to calculate numerical solutions of the radiation transport equations in a static background. The feasibility of the method in all regimes, from diffusion to free-streaming, is demonstrated by a number of numerical tests, and the effect of the choice of the closure relation on the results is discussed.     

Relativistic models of magnetars: the twisted torus magnetic field configuration

We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. Our method is based on the solution of the relativistic Grad–Shafranov equation, to which Maxwell's equations can be reduced. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher-order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.     

Radiation Hydrodynamics in Supernovae

We discuss the current status of our hydrodynamical radiation (HYDRA) code for rapidly expanding, low-density envelopes commonly found in core collapse and thermonuclear supernovae. In supernovae, one of the main issues is the coupling between a radiation field and properties of the matter. Due to the low densities, nonthermal excitation by high-energy photons from radioactive decays and the time dependence of the problem, significant departures from local thermodynamical equilibrium (LTE) are common throughout the envelope even at large optical depths. This effect must be taken into account to simulate the evolution of spectra and light curves which are the basic tools to link between explosion physics and observations. The large velocity fields and the non-LTE problem result in a coupling of spatial, frequency space and the level population. This physical system can be described by a large system of coupled integro-differential equations for which the spatial and energy discretization (and its errors) are coupled. For the numerical solution, we use variable separation, analytic solutions and approximations, and iterative schemes. The need for adaptive mesh refinement (AMR) is demonstrated. As example, we show detailed spectra and light curves for the thermonuclear Supernova SN99by.     

AMR Simulations of Magnetohydrodynamic Problems by the CESE Method in Curvilinear Coordinates

The objective of this paper is to present new extensions of the space – time conservation element and solution element (CESE) method for simulations of magnetohydrodynamic (MHD) problems in general curvilinear coordinates by using an adaptive mesh refinement (AMR) grid system. By transforming the governing MHD equations from the physical space (x,y,z) to the computational space (ξ,η,ζ) while retaining the form of conservation, the CESE method is established for MHD in the curvilinear coordinates. Utilizing the parallel AMR package PARAMESH, we present the first implementation of applying the AMR CESE method for MHD (AMR-CESE-MHD) in both Cartesian and curvilinear coordinates. To show the validity and capabilities of the AMR-CESE-MHD code, a suite of numerical tests in two and three dimensions including ideal MHD and resistive MHD are carried out, with two of them in both Cartesian and curvilinear coordinates. Numerical tests show that our results are highly consistent with those obtained previously by other authors, and the results under both coordinate systems confirm each other very well.     

On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.     

General Relativistic Magnetoionic Theory

We have developed methods for tracing rays and performing radiative transfer through a magneto active plasma in a general relativistic environment. The two electromagnetic plasma modes propagate differently due to a combination of dispersive and gravitational effects. We have found that, when given an appropriate environment surrounding the central black hole, it is indeed possible to generate a significant degree of circular polarisation without an appreciable amount of linear polarisation due to these effects alone.     

Relativistic blast waves and synchrotron emission

Relativistic shocks can accelerate particles by the first-order Fermi mechanism; the particles then emit synchrotron emission in the post-shock gas. This process is of particular interest in the models used for the afterglow of gamma-ray bursts. In this paper we use recent results in the theory of particle acceleration at highly relativistic shocks to model the synchrotron emission in an evolving, inhomogeneous and highly relativistic flow. We have developed a numerical code that integrates the relativistic Euler equations for fluid dynamics with a general equation of state, together with a simple transport equation for the accelerated particles. We present tests of this code and, in addition, we use it to study the gamma-ray burst afterglow predicted by the fireball model, along with the hydrodynamics of a spherically-symmetric relativistic blast wave.
We find that, while broadly speaking the behaviour of the emission is similar to that already predicted with semi-analytic approaches, the detailed behaviour is somewhat different. The 'breaks' in the synchrotron spectrum behave differently with time, and the spectrum above the final break is harder than had previously been expected. These effects are due to the incorporation of the geometry of the (spherical) blast wave, along with relativistic beaming and adiabatic cooling of the energetic particles leading to a mix, in the observed spectrum, between recently injected 'uncooled' particles and the older 'cooled' population in different parts of the evolving, inhomogeneous flow.     

Non-axisymmetric magnetostatic equilibrium

This paper considers the structural properties of a sunspot-like magnetic flux tube which lacks perfect axisymmetry. The flux tube is taken to be in static equilibrium with an atmosphere in a uniform gravity. Assuming the departure from axisymmetry to be slight, the equations for the first order non-axisymmetric part of the equilibrium are derived in cylindrical coordinates. These first order equations reduce to a linear second order hyperbolic partial differential equation in the r-z plane. Whereas Cauchy type boundary conditions are appropriate for hyperbolic equations, physical considerations dictate the specification of boundary conditions on a closed surve for our problem of interest. The construction of solutions to this boundary value problem is illustrated with three analytically soluble cases, where the zero-order axisymmetric equilibria are chosen to have magnetic field geometry of different complexity. A physical discussion of the results is given.     

Relativistic gravitational potential and its relation to mass-energy

From the general theory of relativity a relation is deduced between the mass of a particle and the gravitational field at the position of the particle. For this purpose the fall of a particle of negligible mass in the gravitational field of a massive body is used. After establishing the relativistic potential and its relationship to the rest mass of the particle, we show, assuming conservation of mass-energy, that the difference between two potential-levels depends upon the value of the radial metric coefficient at the position of an observer. Further, it is proved that the relativistic potential is compatible with the general concept of the potential also from the standpoint of kinematics. In the third section it is shown that, although the mass-energy of a body is a function of the distance from it, this does not influence the relativistic potential of the body itself. From this conclusion it follows that the mass-energy of a particle in a gravitational field is anisotropic; isotropic is the mass only. Further, the possibility of an incidental feed-back between two masses is ruled out, and the law of the composition of the relativistic gravitational potentials is deduced. Finally, it is shown, by means of a simple model, that local inhomogeneities in the ideal fluid filling the Universe have negligible influence on the total potential in large regions.     

The signatures of voids — I. Numerical model

In this paper, we describe the ray-tracing code used to calculate the signatures of quasi-linear voids in front of, and on, the last scattering surface. The spherically symmetric, general relativistic, Lagrangian fluid equations are integrated in time along with the geodesic equations. The voids are partially filled and are surrounded by either cold dark matter or interacting fluid with a small amount of pressure. In order to obtain accurate results using smaller arrays, a non-uniform grid is employed.     

Entrainment and Deceleration of Relativistic Jets

Extragalactic radio sources are separated in two classes according to their specific luminosity: Fanaroff-Riley I and II. The origin of this dichotomy can be due either to intrinsec different properties of the AGN or to interaction of the jet with different enviroments. We assume that jets are always relativistic and supersonic close to their source, as recent observations suggest, and we explore the conditions in which the jets decelerate assuming FR I morphology. We have carried out high resolution 3D simulations for a set of parameters and in this paper we concentrate our discussion on two extreme cases.     

天文常数中的相对论问题

现代天文观测技术的日新月异、广义相对论的１ＰＮ近似方法在天体力学和天体测量中的广泛应用,使得有必要在１ＰＮ框架中严格而细致地重新审查天文常数系统。在相对论框架里,太阳系天体的质量应当定义为ＢＤ质量,它们的相对变化不超过１０＾－１９,可视为守恒量;引力势满足的方程不再是Ｐｏｉｓｓｏｎ方程而与坐标规范的选择有关,引力势也不再能用传统的球谐函数展开。应当选定一种规范,并且以ＢＤ多极矩作为天文常数。黄赤交     

Relativistic reductions for radiointerferometric observables

The special and general relativistic corrections for the basic radiointerferometric observables —time-delay and fringe frequency — are studied with an accuracy of the order of 5×10^?10 (‘post-Newtonian approximation’).     

General relativistic analysis of structure and stability of charged fluid disks around compact objects

In this paper we give a detailed general relativistic formulation of the study of structure and stability of charged fluid disks around compact objects like black holes neglecting the self-gravitation of the disk itself. Having presented the general equations for equilibrium as well as for perturbations we solve explicitly the cases of rigidly and differentially rotating thin disks, with constant charge density and zero pressure, confined to the equatorial plane of the black hole. By using normal mode analysis we have analysed the stability of such disks under purely radial perturbations and find that the disks are generally stable. On leave of absence from Government College, Jagadalpur 494005     

General relativistic self-similar solutions in cosmology

We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, p , and energy density, μ, in the shock-heated matter are assumed to obey   p = w μ  , where w is a positive constant. Consistent solutions are found for shocks propagating from the symmetry centre of a region of a positive density excess over the background. In these solutions, shocks exist outside the radius marking the event horizon of the black hole which would be present in a shock-less collapse. For large jumps in the energy density at the shock, a black hole is avoided altogether and the solutions are regular at the centre. The shock-heated gas does not contain any sonic points, provided the motion of the cold gas ahead of the shock deviates significantly from the Hubble flow. For shocks propagating in the uniform background, sonic points always appear for small jumps in the energy density. We also discuss self-similar solutions without shocks in fluids with   w < −1/3  .