In this paper, we extend the unified kinetic particle (UGKP) method to the frequency-dependent radiative transfer equation with both absorption-emission and scattering processes. The extended UGKP method could not only capture the diffusion and free transport limit, but also provide a smooth transition in the physical and frequency space in the regime between the above two limits. The proposed scheme has the properties of asymptotic-preserving, regime-adaptive, and entropy-preserving, which make it an accurate and efficient scheme in the simulation of multiscale photon transport problems. The methodology of scheme construction is a coupled evolution of macroscopic energy equation and the microscopic radiant intensity equation, where the numerical flux in macroscopic energy equation and the closure in microscopic radiant intensity equation are constructed based on the integral solution. Both numerical dissipation and computational complexity are well controlled especially in the optical thick regime. A 2D multi-thread code on a general unstructured mesh has been developed. Several numerical tests have been simulated to verify the numerical scheme and code, covering a wide range of flow regimes. The numerical scheme and code that we developed are highly demanded and widely applicable in the high energy density engineering applications.

翻译：本文我们将统一动力学粒子（UGKP）方法推广至同时包含吸收-发射与散射过程的频率依赖辐射传输方程。改进后的UGKP方法不仅能够捕捉扩散和自由输运极限，还能在上述两个极限之间的物理和频率空间提供平滑过渡。所提出的格式具有渐进保持、工况自适应和熵保持的特性，使其成为多尺度光子输运问题模拟中精确且高效的数值格式。该格式的构建方法基于宏观能量方程与微观辐射强度方程的耦合演化，其中宏观能量方程中的数值通量和微观辐射强度方程中的闭合关系均基于积分解构建。数值耗散与计算复杂度在光学厚区域均得到有效控制。我们开发了适用于一般非结构网格的二维多线程代码，并通过涵盖广泛流态范围的多个数值测试验证了数值格式与代码的正确性。所开发的数值格式与代码在高能量密度工程应用中具有重要需求与广阔应用前景。