  The multi-frequency radiation transport equation (RTE) system models the
photon transport and the energy exchange process between the background
material and different frequency photons. In this paper, the unified
gas-kinetic wave-particle (UGKWP) method for multi-frequency RTE is developed
to capture the multiscale non-equilibrium transport in different optical
regimes. In the UGKWP, a multiscale evolution process is properly designed to
obtain both non-equilibrium transport in the optically thin regime and thermal
diffusion process in the optically thick regime automatically. At the same
time, the coupled macroscopic energy equations for the photon and material are
solved implicitly by the matrix-free source iteration method. With the
wave-particle decomposition strategy, the UGKWP method has a dynamic adaptivity
for different regime physics. In the optically thick regime, no particles will
be sampled in the computational domain and the thermal diffusion solution for
the photon transport will be recovered. While in the optically thin regime,
stochastic particles will play a dominant role in the evolution and the
non-equilibrium free transport of photon is automatically followed. In the
frequency-dependent transport, the frequency carried by the simulating particle
will be determined by a linear-frequency sampling strategy. In addition, to
better resolve the sharp of opacity in the photon transport across a cell
interface, the free streaming time of simulating particle in the UGKWP method
will be reset when it passes through the interface. Moreover, the numerical
relaxation time is properly defined to increase the particle proportion in the
sharp opacity transition region in order to avoid numerical oscillation.
Several typical test cases for the RTE system have been calculated to
demonstrate the accuracy and reliability of the current frequency-dependent
UGKWP method.
