标题： 自适应时间步长的超级液滴方法蒙特卡罗碰撞凝聚方案 显示英文标题

标题： Adaptive time-stepping for the Super-Droplet Method Monte Carlo collision-coalescence scheme

摘要： 我们对超级液滴方法（SDM）的自适应时间步长方案进行了分析，SDM 是一种用于模拟粒子凝聚的蒙特卡洛算法。SDM 将云滴表示为加权超级液滴，能够实现对微物理过程（如碰撞-合并）的高保真表示。然而，当预期的事件数量在超级液滴配置下不可实现时，该算法可能会低估碰撞次数，从而引入一种称为碰撞不足的偏差误差。尽管 SDM 展现了蒙特卡洛方案固有的统计波动，但这种不足是一种对碰撞事件的系统性低估。这种误差可以通过自适应时间步长来解决，自适应时间步长动态调整模拟时间步长以消除这种不足。我们分析了在广泛的时间步长、超级液滴数量和初始化策略下该不足的表现，并探讨了准确性和效率之间的权衡。使用经典的 Safranov-Golovin 测试案例，我们表明不足随着时间步长和超级液滴数量的增加而增加，并且自适应时间步长可以有效地消除相关误差，而不会带来显著的成本。我们测试了一种平滑的初始分布范围，其极值代表两种不同的初始化方法，并发现尽管不足对属性空间采样策略的选择敏感，但自适应时间步长显著减少了差异，使得用户可以选择针对其他过程优化的初始化方法。我们还提出了一种可视化方法，利用网络连通性图同时捕捉属性采样、多个时间步长内的液滴相互作用以及不足。在二维流动耦合模拟中，我们发现不足的影响比之前显示的更强，未经纠正的不足会延迟降水的发生。 显示英文摘要

摘要： We present an analysis of an adaptive time-stepping scheme for the Super-Droplet Method (SDM), a Monte Carlo algorithm for simulating particle coagulation. SDM represents cloud droplets as weighted superdroplets, enabling high-fidelity representations of microphysical processes such as collision-coalescence. However, the algorithm can undercount collisions when the expected number of events is not realizable given the superdroplet configuration, introducing a biased error referred here as the collision deficit. While SDM exhibits statistical spread inherent to Monte Carlo schemes, the deficit is a systematic underestimation of collision events. This error can be addressed with adaptive time-stepping, which dynamically adjusts simulation time steps to eliminate this deficit. We analyze the behavior of the deficit across a wide range of timesteps, superdroplet counts, and initialization strategies, and explore trade-offs between accuracy and efficiency. Using the classical Safranov-Golovin test case, we show that the deficit increases with timestep and superdroplet count, and that adaptive time-stepping effectively removes the associated error without significant cost. We test a smooth continuum of initial distributions with extrema representing two different initialization methods, and find that while the deficit is sensitive to the choice of attribute-space sampling strategies, adaptive time-stepping substantially reduces the difference, allowing for users to choose initialization methods optimized for other processes. We also propose a method of visualization, capturing both the attribute sampling, droplet interactions over multiple timesteps, and the deficit using network connectivity graphs. In 2-D flow-coupled simulations, we find the deficit can have a stronger effect on convergence than previously shown, with uncorrected deficit delaying the onset of precipitation.