多尺度动理学输运的波-粒子分解框架：连续谱方程与耦合波-粒子迭代

中文摘要 AI 辅助

波-粒子分解被提出作为一个多尺度动理学输运的框架，包含一个理论和一个算法。沿着动理学方程的特征线，解在局部动理学视界上的平衡积分定义了一个波，该波仅依赖于守恒变量，而其精确补集定义了一个粒子。两者均满足矩为扩展纳维-斯托克斯方程的动理学方程，守恒定律与粒子方程一起构成一个封闭系统，该系统对每个视界都等价于动理学方程。以视界与弛豫时间之比为参数，这些系统形成一个从动理学理论到纳维-斯托克斯流体动力学的连续谱，该谱逐单元适应流动。该算法是针对定常流动的耦合波-粒子迭代。它交替进行守恒变量的宏观迭代（粒子冻结）和粒子的动理学迭代（波固定）。其不动点是离散动理学解，具有渐近保持性，其近连续收敛因子受粒子所承载输运份额的限制，该份额随视界-弛豫比指数衰减。碰撞模型仅通过一个守恒余项进入，方程和迭代针对Bhatnagar-Gross-Krook、Shakhov和椭球统计模型、玻尔兹曼和朗道方程、中子输运和辐射输运写出。该分解与统一气体动理学波-粒子方法、微观-宏观分解、罚方法和合成加速相关。对圆柱绕流和三维X38飞行器周围高超声速流动的计算说明了分布的分割如何适应流动以及迭代被加速的强度。

英文摘要

The wave-particle decomposition is presented as a framework for multiscale kinetic transport, comprising a theory and an algorithm. Along the characteristics of the kinetic equation, the equilibrium integral of the solution over a local kinetic horizon defines a wave, which depends only on the conservative variables, and its exact complement defines a particle. Both obey kinetic equations whose moments are extended Navier-Stokes equations, and the conservation laws together with the particle equation form a closed system that is equivalent to the kinetic equation for every horizon. Parametrized by the ratio of the horizon to the relaxation time, these systems form a continuous spectrum from kinetic theory to Navier-Stokes hydrodynamics that adapts to the flow from cell to cell. The algorithm is a coupled wave-particle iteration for steady flows. It alternates a macroscopic iteration for the conservative variables, with the particle frozen, and a kinetic iteration for the particle, with the wave fixed. Its fixed point is the discrete kinetic solution, it is asymptotic preserving, and its near-continuum convergence factor is bounded by the share of the transport carried by the particle, a share that decays exponentially with the horizon-to-relaxation ratio. The collision model enters only through a conservative remainder, and the equations and the iteration are written out for the Bhatnagar-Gross-Krook, Shakhov and ellipsoidal statistical models, the Boltzmann and Landau equations, neutron transport and radiative transfer. The decomposition is related to the unified gas-kinetic wave-particle method, the micro-macro decomposition, penalization and synthetic acceleration. Computations of hypersonic flows past a cylinder and around the three-dimensional X38 vehicle illustrate how the division of the distribution adapts to the flow and how strongly the iteration is accelerated.

发表机构

• Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）
• Hong Kong University of Science and Technology（香港科技大学）

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