HARM uses a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. On smooth flows HARM converges at second order.

HAM solves non-relativistic hyperbolic partial differential equations in conservative form using high-resolution shock-capturing techniques. This version of HAM has been configured to solve the magnetohydrodynamic equations of motion in axisymmetry to evolve a shearing box model.

The efficiency of thin disk accretion onto black holes depends on the inner boundary condition, specifically the torque applied to the disk at the last stable orbit. This is usually assumed to vanish. This code estimates the torque on a magnetized disk using a steady magnetohydrodynamic inflow model originally developed by Takahashi et al. The efficiency e can depart significantly from the classical thin disk value. In some cases e > 1, i.e., energy is extracted from the black hole.

ORBADV adopts a ZEUS-like scheme to solve magnetohydrodynamic equations of motion in a shearing sheet. The magnetic field is discretized on a staggered mesh, and magnetic field variables represent fluxes through zone faces. The code uses obital advection to ensure fast and accurate integration in a large shearing box.

TwoDSSM solves the equations of self-gravitating hydrodynamics in the shearing sheet, with cooling. TwoDSSM is configured to use a simple, exponential cooling model, although it contains code for a more complicated (and perhaps more realistic) cooling model based on a one-zone vertical model. The complicated cooling model can be switched on using a flag.

Conservative numerical schemes for general relativistic magnetohydrodynamics (GRMHD) require a method for transforming between "conserved'' variables such as momentum and energy density and "primitive" variables such as rest-mass density, internal energy, and components of the four-velocity. The forward transformation (primitive to conserved) has a closed-form solution, but the inverse transformation (conserved to primitive) requires the solution of a set of five nonlinear equations. This code performs the inversion.

grmonty is a Monte Carlo radiative transport code intended for calculating spectra of hot, optically thin plasmas in full general relativity. The code models hot accretion flows in the Kerr metric, it incorporates synchrotron emission and absorption and Compton scattering. grmonty can be readily generalized to account for other radiative processes and an arbitrary spacetime.

Harmony is a general numerical scheme for evaluating MBS emission and absorption coefficients for both polarized and unpolarized light in a plasma with a general distribution function.

Bessel, written in the C programming language, uses an accurate scheme for evaluating Bessel functions of high order. It has been extensively tested against a number of other routines, demonstrating its accuracy and efficiency.

VHD is a numerical study of viscous fluid accretion onto a black hole. The flow is axisymmetric and uses a pseudo-Newtonian potential to model relativistic effects near the event horizon. VHD is based on ZEUS-2D (Stone & Norman 1992) with the addition of an explicit scheme for the viscosity.

GRIM (General Relativistic Implicit Magnetohydrodynamics) evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. GRIM, which runs on CPUs as well as on GPUs, combines time evolution and primitive variable inversion needed for conservative schemes into a single step using only the residuals of the governing equations as inputs. This enables the code to be physics agnostic as well as flexible regarding time-stepping schemes.

ipole is a ray-tracing code for covariant, polarized radiative transport particularly useful for modeling Event Horizon Telescope sources, though may also be used for other relativistic transport problems. The code extends the ibothros scheme for covariant, unpolarized transport using two representations of the polarized radiation field: in the coordinate frame, it parallel transports the coherency tensor, and in the frame of the plasma, it evolves the Stokes parameters under emission, absorption, and Faraday conversion. The transport step is as spacetime- and coordinate- independent as possible; the emission, absorption, and Faraday conversion step is implemented using an analytic solution to the polarized transport equation with constant coefficients. As a result, ipole is stable, efficient, and produces a physically reasonable solution even for a step with high optical depth and Faraday depth.

EBHLIGHT (also referred to as BHLIGHT) solves the equations of general relativistic radiation magnetohydrodynamics in stationary spacetimes. Fluid integration is performed with the second order shock-capturing scheme HARM (ascl:1209.005) and frequency-dependent radiation transport is performed with the second order Monte Carlo code grmonty (ascl:1306.002). Fluid and radiation exchange four-momentum in an explicit first-order operator-split fashion.