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.

翻译：本文提出了一种无需时间步长约束的隐式统一气体动理学波粒方法。在可接受的时间分辨率下，库朗数可设置至尽可能大。该方法无需对分布函数施加任何人工封闭形式，即可精确捕捉非平衡输运流动物理。方案演化过程由两个时间参数控制，即物理时间步长分辨率和数值时间步长分辨率。基于物理时间步长分辨率，将构建离散形式控制方程，其中真实非平衡流动物理的演化不依赖于数值推进时间步长的变化。波粒分解及其演化遵循熵满足过程。除物理解对数值时间步长具有不变性外，该隐式统一气体动理学波粒方法在物理解表征中还具有渐近保持特性和全尺度自适应复杂度。开发了多维二维和三维算法，并应用于惯性约束聚变的工程问题。同时包含其他多尺度算例，以验证该方法对多尺度非平衡输运的捕捉能力。