统一气体动力学波粒方法IV：多组分气体混合物和等离子体输运
Unified Gas-kinetic Wave-Particle Method IV: Multi-species Gas Mixture and Plasma Transport
摘要：
本文将统一气体动力学波粒（UGKWP）方法推广到多组分气体混合和多尺度等离子体输运问题。该格式的构造基于网格尺寸和时间步长的直接建模，局部单元的努森数决定了流动物理性质。该方案具有多尺度和渐近复杂度递减特性。多尺度特性意味着根据单元的Knudsen数，该方案可以捕获稀薄流区的非平衡流动物理，并保持连续流区的渐近Euler，Navier-Stokes和磁流体力学极限。渐近复杂性递减性质意味着格式的总自由度随着单元格Knudsen数的减小而自动减小。在连续体区域，该方案自动从动力学求解器退化为流体动力学求解器。在UGKWP中，微观速度分布的演化与宏观变量的演化相耦合，颗粒演化以及宏观通量从时间累积解到时间步长尺度从动力学模型方程来模拟。对于等离子体输运，电流方案提供了一个平滑的过渡，从粒子在细胞（PIC）的方法在稀薄的制度，磁流体动力学（MHD）求解器在连续制度。在连续极限下，UGKWP方法的网格尺寸和时间步长不限于小于平均自由程和平均碰撞时间。在强磁化区，晶胞尺寸和时间步长不受德拜长度和等离子体回旋周期的限制。在多个流态下的数值试验验证了该格式的多尺度性和渐近复杂性减小性。
英文摘要：
In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step scales, and the local cell's Knudsen number determines the flow physics. The proposed scheme has the multiscale and asymptotic complexity diminishing properties. The multiscale property means that according to cell's Knudsen number the scheme can capture the non-equilibrium flow physics in the rarefied flow regime, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics limit in the continuum regime. The asymptotic complexity diminishing property means that the total degree of freedom of the scheme automatically decreases as cell's Knudsen number decreases. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In UGKWP, the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables, and the particle evolution as well as the macroscopic fluxes are modeled from the time accumulating solution up to a time step scale from the kinetic model equation. For plasma transport, current scheme provides a smooth transition from particle in cell (PIC) method in the rarefied regime to the magnetohydrodynamic (MHD) solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method is not restricted to be less than the mean free path and mean collision time. In the highly magnetized regime, the cell size and time step are not restricted by the Debye length and plasma cyclotron period. The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.
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