Related papers: Relativistic MHD and black hole excision: Formulat…
Astrophysical plasmas in relativistic spacetimes, such as black hole accretion flows, are often weakly collisional and require kinetic modeling to capture non-local transport and particle acceleration. However, the extreme scale separation…
A considerable amount of attention has been given to discontinuous Galerkin methods for hyperbolic problems in numerical relativity, showing potential advantages of the methods in dealing with hydrodynamical shocks and other…
Einstein equations projected on black-hole horizons give rise to the equations of motion of a viscous fluid. This suggests a way to understand the microscopic degrees of freedom on the black-hole horizon by focusing on the physics of this…
Through full solvability of 2+1 dimensional general relativity we derive out exact dynamic inner metric of collapsing stars with inhomogeneous initial mass distribution but joining with outside Anti-deSitt-Schwarzschild black holes…
Numerical simulation of magnetohydrodynamic (MHD) turbulence makes it possible to study accretion dynamics in detail. However, special effort is required to connect inflow dynamics (dependent largely on angular momentum transport) to…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper (hep-th/0305147) to a charged black hole background whose horizon is described by an…
Observational evidence and many numerical simulations show the existence of wind (i.e., uncollimated outflow) in accretion systems of the elliptical galaxy center. One of the primary aims of this study is to investigate the solutions of…
The elliptic 2-Hessian equation is a fully nonlinear partial differential equation (PDE) that is related to intrinsic curvature for three dimensional manifolds. We introduce two numerical methods for this PDE: the first is provably…
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…
The Event Horizon Telescope (EHT) has imaged the shadow of the supermassive black hole in M87. A library of general relativistic magnetohydrodynamics (GMRHD) models was fit to the observational data, providing constraints on black hole…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
In this paper, a few dual least-squares finite element methods and their application to scalar linear hyperbolic problems are studied. The purpose is to obtain $L^2$-norm approximations on finite element spaces of the exact solutions to…
This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified…
We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics (GRRMHD) using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is…
Two quasi local approaches to black holes are combined: Near Horizon Geometries (NHG) and stationary Black Hole Holographs (BHH). Necessary and sufficient conditions on BHH data for the emergence of NHGs as resulting vacuum solutions to…
We propose a new method of detecting Ellis wormholes by use of the images of wormholes surrounded by optically thin dust. First, we derive steady solutions of dust and more general medium surrounding the wormhole by solving relativistic…
This work presents an extension of discretely entropy stable discontinuous Galerkin (DG) methods to the resistive magnetohydrodynamics (MHD) equations. Although similar to the compressible Navier-Stokes equations at first sight, there are…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such…