Department of Physics, North Dakota State University, P.O. Box 6050, Fargo, ND 58108, USA.
Phys Chem Chem Phys. 2009 Nov 14;11(42):9667-76. doi: 10.1039/b910356b. Epub 2009 Aug 19.
Particle-based simulation methods for fluid flow follow a discrete time dynamics of subsequent streaming and collision events. The algorithm considered here, called stochastic rotation dynamics, involves collisions between an arbitrary number of partners; all particles that happen to be in the same cell of a randomly positioned grid interact at once by prescribed rules. I show, in two dimensions, how a multi-particle generalization of the Enskog equation can be derived from the Liouville equation and how the hydrodynamic equations can be obtained by a Chapman-Enskog expansion. The resulting macroscopic equations contain a collisional contribution to the transport coefficients, absent in earlier Chapman-Enskog approaches, which agrees exactly with previously known results from other kinetic theories. This approach opens up a powerful, systematic route to deriving hydrodynamic equations for particle-based models, which is generalizable to models with active particles.
基于粒子的流体流动模拟方法遵循后续流动和碰撞事件的离散时间动力学。这里考虑的算法称为随机旋转动力学，涉及任意数量的伙伴之间的碰撞；所有碰巧位于随机位置网格的同一单元格中的粒子都可以通过规定的规则立即相互作用。我在二维空间中展示了如何从刘维尔方程推导出 Enskog 方程的多粒子推广，以及如何通过 Chapman-Enskog 展开得到流体力学方程。所得的宏观方程包含了输运系数的碰撞贡献，这在早期的 Chapman-Enskog 方法中是不存在的，它与来自其他动力学理论的先前已知结果完全一致。这种方法为基于粒子的模型推导出流体力学方程开辟了一条强大而系统的途径，该方法可推广到具有活性粒子的模型。
