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In this work, we present a unified gas-kinetic particle (UGKP) method for thesimulation of multiscale photon transport. The multiscale nature of theparticle method mainly comes from the recovery of the time evolution fluxfunction in the unified gas-kinetic scheme (UGKS) through a coupled dynamicprocess of particle transport and collision. This practice improves theoriginal operator splitting approach in the Monte Carlo method, such as theseparated treatment of particle transport and collision. As a result, with thevariation of the ratio between numerical time step and local photon's collisiontime, different transport physics can be fully captured in a singlecomputation. In the diffusive limit, the UGKP method could recover the solutionof the diffusion equation with the cell size and time step being much largerthan the photon's mean free path and the mean collision time. In the freetransport limit, it presents an exact particle tracking process as the originalMonte Carlo method. In the transition regime, the weights of particle freetransport and collision are determined by the ratio of local numerical timestep to the photon's collision time. Several one-dimensional numerical examplescovering all transport regimes from the optically thin to optically thick arecomputed to validate the accuracy and efficiency of the current scheme. Incomparison with the $S_N$ discrete ordinate method, the UGKP method is based onparticles and avoids the discretization of particle velocity space, which doesnot suffer from the ray effect.

A Unified Gas-kinetic Particle Method for Multiscale Photon Transport