A Unified Gas-kinetic Particle Method for Multiscale Photon Transport
This work provides a novel particle-based method for simulating multiscale photon transport that overcomes the ray effect issue of discrete ordinate methods, benefiting computational physics and engineering applications involving radiative transfer.
The paper introduces a unified gas-kinetic particle (UGKP) method for multiscale photon transport that recovers the time evolution flux function through coupled particle transport and collision, enabling accurate simulation across all transport regimes from optically thin to thick. The method avoids ray effects and matches solutions of the diffusion equation in the diffusive limit while preserving exact particle tracking in the free transport limit.
In this work, we present a unified gas-kinetic particle (UGKP) method for the simulation of multiscale photon transport. The multiscale nature of the particle method mainly comes from the recovery of the time evolution flux function in the unified gas-kinetic scheme (UGKS) through a coupled dynamic process of particle transport and collision. This practice improves the original operator splitting approach in the Monte Carlo method, such as the separated treatment of particle transport and collision. As a result, with the variation of the ratio between numerical time step and local photon's collision time, different transport physics can be fully captured in a single computation. In the diffusive limit, the UGKP method could recover the solution of the diffusion equation with the cell size and time step being much larger than the photon's mean free path and the mean collision time. In the free transport limit, it presents an exact particle tracking process as the original Monte Carlo method. In the transition regime, the weights of particle free transport and collision are determined by the ratio of local numerical time step to the photon's collision time. Several one-dimensional numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the current scheme. In comparison with the $S_N$ discrete ordinate method, the UGKP method is based on particles and avoids the discretization of particle velocity space, which does not suffer from the ray effect.