An entropy preserving implicit unified gas-kinetic wave-particle method for radiative transport equation

In this paper, an implicit unified gas-kinetic wave-particle method is developed without the time step constraint. Under the acceptable temporal resolution, the Courant number can be set as large as possible. Non-equilibrium transport flow physics can be accurately captured without imposing any artificial closure form of the distribution function. The evolution process of the scheme is controlled by two temporal parameters, namely the physical time step resolution and the numerical time step resolution. Based on the physical time step resolution, the governing equations in a discretized form will be constructed, where the evolution of the genuinely non-equilibrium flow physics will not depend on the variation of the numerical marching time step. The wave-particle decomposition and their evolution follow an entropy-satisfying process. Besides the invariance of the physical solution on the numerical time step, the implicit unified gas-kinetic wave-particle method has also asymptotic-preserving property and regime-adaptive complexity in the representation of the physical solution. Multidimensional 2D and 3D algorithms are developed and used in the engineering applications of inertial confinement fusion. Other multiscale tests are also included to validate the numerical method for the capturing of multi-scale non-equilibrium transport.