  Hot, diffuse, relativistic plasmas such as sub-Eddington black hole accretion
flows are expected to be collisionless, yet are commonly modeled as a fluid
using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative
effects such as heat conduction and viscosity can be important in a
collisionless plasma and will potentially alter the dynamics and radiative
properties of the flow from that in ideal fluid models; we refer to models that
include these processes as Extended GRMHD. Here we describe a new conservative
code, grim, that enables all the above and additional physics to be efficiently
incorporated. grim combines time evolution and primitive variable inversion
needed for conservative schemes into a single step using an algorithm that only
requires the residuals of the governing equations as inputs. This algorithm
enables the code to be physics agnostic as well as flexibility regarding
time-stepping schemes. grim runs on CPUs, as well as on GPUs, using the same
code. We formulate a performance model, and use it to show that our
implementation runs optimally on both architectures. grim correctly captures
classical GRMHD test problems as well as a new suite of linear and nonlinear
test problems with anisotropic conduction and viscosity in special and general
relativity. As tests and example applications, we resolve the shock
substructure due to the presence of dissipation, and report on relativistic
versions of the magneto-thermal instability and heat flux driven buoyancy
instability, which arise due to anisotropic heat conduction, and of the
firehose instability, which occurs due to anisotropic pressure (i.e.
viscosity). Finally, we show an example integration of an accretion flow around
a Kerr black hole, using Extended GRMHD.
