The unified gas-kinetic wave-particle method (UGKWP) has been developed for the multiscale gas, plasma, and multiphase flow transport processes for the past years. In this work, we propose an implicit unified gas-kinetic wave-particle (IUGKWP) method to remove the CFL time step constraint. Based on the local integral solution of the radiative transfer equation (RTE), the particle transport processes are categorized into the long-$\lambda$ streaming process and the short-$\lambda$ streaming process comparing to a local physical characteristic time $t_p$. In the construction of the IUGKWP method, the long-$\lambda$ streaming process is tracked by the implicit Monte Carlo (IMC) method; the short-$\lambda$ streaming process is evolved by solving the implicit moments equations; and the photon distribution is closed by a local integral solution of RTE. In the IUGKWP method, the multiscale flux of radiation energy and the multiscale closure of photon distribution are constructed based on the local integral solution. The IUGKWP method preserves the second-order asymptotic expansion of RTE in the optically thick regime and adapts its computational complexity to the flow regime. The numerical dissipation is well controlled, and the teleportation error is significantly reduced in the optically thick regime. The computational complexity of the IUGKWP method decreases exponentially as the Knudsen number approaches zero, and the computational efficiency is remarkably improved in the optically thick regime. The IUGKWP is formulated on a generalized unstructured mesh, and multidimensional 2D and 3D algorithms are developed. Numerical tests are presented to validate the capability of IUGKWP in capturing the multiscale photon transport process. The algorithm and code will apply in the engineering applications of inertial confinement fusion (ICF).

翻译：统一气体动理学波粒方法（UGKWP）在过去数年间已被发展用于多尺度气体、等离子体及多相流输运过程。在本工作中，我们提出一种隐式统一气体动理学波粒（IUGKWP）方法，以消除CFL时间步长约束。基于辐射输运方程（RTE）的局部积分解，粒子输运过程根据与局部物理特征时间$t_p$的比较被分类为长$\lambda$流输运过程与短$\lambda$流输运过程。在IUGKWP方法的构建中，长$\lambda$流输运过程通过隐式蒙特卡罗（IMC）方法追踪；短$\lambda$流输运过程通过求解隐式矩方程演化；光子分布通过RTE的局部积分解封闭。在IUGKWP方法中，辐射能量的多尺度通量与光子分布的多尺度封闭基于局部积分解构建。该方法在光学厚区域保持RTE的二阶渐近展开，并使其计算复杂度自适应于流动状态。数值耗散得到良好控制，且在光学厚区域中远距离输运误差显著降低。IUGKWP方法的计算复杂度随Knudsen数趋近于零呈指数下降，计算效率在光学厚区域显著提升。该方法在广义非结构化网格上建立，并发展了多维二维与三维算法。通过数值测试验证了IUGKWP在捕捉多尺度光子输运过程方面的能力，该算法与代码将应用于惯性约束聚变（ICF）的工程实践。