In this work, we propose a unified gas kinetic particle (UGKP) method for solving the nonlinear thermal radiative transfer equations. The UGKP method is a multiscale method in that the macro and microscopic variables are coupled and updated in a consistent way. It employs a finite volume formulation for the macroscopic variable evolution, and a particle-based Monte Carlo solver for tracking the non-equilibrium transport. The stiff coupling between the radiation and material energy is included and resolved efficiently by the coupled macroscopic equations. Compared with the implicit Monte Carlo (IMC) method, it does not employ the effective scattering events. Moreover, we demonstrate that the UGKP method has the asymptotic preserving property in capturing the diffusion limit in optically thick regions. Numerical simulations show that our method is comparable in computational cost to the IMC method for optically thin problems, and becomes much more efficient for optically thick problems. More importantly, the UGKP method doesn't require the cell size being less than the photon's mean free path and it achieves the highest efficiency in the optically thin and thick regions self-adaptively.

在这项工作中，我们提出了统一的气体动力学粒子（UGKP）方法来求解非线性热辐射传递方程。UGKP方法是一种多尺度方法，其中宏变量和微观变量以一致的方式耦合和更新。它采用有限体积公式进行宏观变量演化，并使用基于粒子的蒙特卡洛求解器跟踪非平衡传输。辐射和材料能量之间的刚性耦合被包括在内，并通过耦合的宏观方程式有效地解析。与隐式蒙特卡洛（IMC）方法相比，它没有采用有效的散射事件。此外，我们证明了UGKP方法在捕获光学较厚区域的扩散极限时具有渐近保持性。数值模拟表明，对于光学较薄的问题，我们的方法在计算成本上可与IMC方法相提并论，对于光学较厚的问题，该方法变得更加有效。更重要的是，UGKP方法并不需要像元大小小于光子的平均自由程，它可以在光学上较薄和较厚的区域自适应地实现最高效率。