Monte Carlo-based relativistic radiation hydrodynamics code with a higher-order scheme

We develop a new relativistic radiation hydrodynamics code based on the Monte Carlo algorithm. In this code, we implement a new scheme to achieve the second-order accuracy in time in the limit of a large packet number for solving the interaction between matter and radiation. This higher-order time-integration scheme is implemented in the manner to guarantee the energy-momentum conservation to the precision of the geodesic integrator. The spatial dependence of radiative processes, such as the packet propagation, emission, absorption, and scattering, are also taken into account up to the second-order accuracy. We validate our code by solving various test problems on a fixed-background metric following the previous studies; one-zone thermalization, dynamical diffusion, radiation dragging, radiation-mediated shock-tube, shock-tube in the optically-thick limit, and Eddington limit problems. We show that our code reproduces physically appropriate results with reasonable accuracy and also demonstrate that the second-order accuracy in time and space is indeed achieved with our implementation for one-zone and one-dimensional problems.