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Abstract Gamma-ray burst (GRB) afterglows are emissions from ultrarelativistic blast waves produced by a narrow jet interacting with surrounding matter. Since the first multimessenger observation of a neutron star merger, hydrodynamic modeling of GRB afterglows for structured jets with smoothly varying angular energy distributions has gained increased interest. While the evolution of a jet is well described by self-similar solutions in both ultrarelativistic and Newtonian limits, modeling the transitional phase remains challenging. This is due to the nonlinear spreading of a narrow jet to a spherical configuration and the breakdown of self-similar solutions. Analytical models are limited in capturing these nonlinear effects, while relativistic hydrodynamic simulations are computationally expensive, which restricts the exploration of various initial conditions. In this work, we introduce a reduced hydrodynamic model that approximates the blast wave as an infinitely thin two-dimensional surface. Further assuming axial symmetry, this model simplifies the simulation to one dimension and drastically reduces the computational costs. We have compared our modeling to relativistic hydrodynamic simulations and semianalytic methods, and applied it to fit the light curve and flux centroid motion of GRB 170817A. These comparisons demonstrate good agreement and validate our approach. We have developed this method into a numerical tool,jetsimpy, which models the synchrotron GRB afterglow emission from a blast wave with arbitrary angular energy and Lorentz factor distribution. Although the code is built with GRB afterglow in mind, it applies to any relativistic jet. This tool is particularly useful in Markov Chain Monte Carlo studies and is provided to the community. 

Abstract We have performed numerical calculations of a binary interacting with a gas disk, using 11 different numerical methods and a standard binary−disk setup. The goal of this study is to determine whether all codes agree on a numerically converged solution and to determine the necessary resolution for convergence and the number of binary orbits that must be computed to reach an agreed-upon relaxed state of the binary−disk system. We find that all codes can agree on a converged solution (depending on the diagnostic being measured). The zone spacing required for most codes to reach a converged measurement of the torques applied to the binary by the disk is roughly 1% of the binary separation in the vicinity of the binary components. For our disk model to reach a relaxed state, codes must be run for at least 200 binary orbits, corresponding to about a viscous time for our parameters, 0.2(a²Ω_B/ν) binary orbits, whereνis the kinematic viscosity. The largest discrepancies between codes resulted from the dimensionality of the setup (3D vs. 2D disks). We find good agreement in the total torque on the binary between codes, although the partition of this torque between the gravitational torque, orbital accretion torque, and spin accretion torque depends sensitively on the sink prescriptions employed. In agreement with previous studies, we find a modest difference in torques and accretion variability between 2D and 3D disk models. We find cavity precession rates to be appreciably faster in 3D than in 2D.