The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD computer code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Potential applications and caveats to the usage of LD are included as a summary.

Langevin动力学（LD）方法（在文献中也称为Brownian Dynamics）通常用于模拟气溶胶颗粒轨迹，以计算传输速率常数，并了解内部和外部流体流动中的气溶胶颗粒迁移情况。本教程旨在说明设置气溶胶颗粒总数的LD模拟的方法学细节，并从一组经典轨迹中得出速率常数。我们讨论了平移Langevin方程的适用性和局限性，以模拟力或流体流场中粒子的组合的随机和确定性运动。详细讨论了出现在Langevin方程中的拉力和随机“扩散”力项，以及与气溶胶系统有关的共同力的摘要（静电，重力，范德华力等）；给出了线性随机常微分方程的常用一阶和四阶Runge-Kutta时间步长方案。为了说明，使用了MATLAB®LD计算机代码的实现，用于使用一级方案模拟重力作用下的粒子沉降。通过两种特定的气溶胶过程展示了气溶胶传输过程的尺度分析以及轨迹模拟的时间步长和域大小的选择：颗粒扩散带电和凝聚。包含一阶和四阶时间步移方案的Fortran®实施方案，用于模拟周期域中粒子的3D运动。