  We present the first numerical analysis of causal, stable first-order
relativistic hydrodynamics with ideal gas microphysics, based in the formalism
developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK
approach provides definitions for the conserved stress-energy tensor and baryon
current, and rigorously proves causality, local well-posedness, strong
hyperbolicity, and linear stability (about equilibrium) for the equations of
motion, subject to a set of coupled nonlinear inequalities involving the
undetermined model coefficients (the choice for which defines the "hydrodynamic
frame"). We present a class of hydrodynamic frames derived from the
relativistic ideal gas "gamma-law" equation of state which satisfy the BDNK
constraints, and explore the properties of the resulting model for a series of
(0+1)D and (1+1)D tests in 4D Minkowski spacetime. These tests include a
comparison of the dissipation mechanisms in Eckart, BDNK, and
Muller-Israel-Stewart theories, as well as investigations of the impact of
hydrodynamic frame on the causality and stability properties of Bjorken flow,
planar shockwave, and heat flow solutions.
