Monte Carlo simulations of two-component drop growth by stochastic coalescence

Abstract

Abstract. The evolution of two-dimensional drop distributions is simulated in this study using a Monte Carlo method. The stochastic algorithm of Gillespie (1976) for chemical reactions in the formulation proposed by Laurenzi et al. (2002) was used to simulate the kinetic behavior of the drop population. Within this framework, species are defined as droplets of specific size and aerosol composition. The performance of the algorithm was checked by a comparison with the analytical solutions found by Lushnikov (1975) and Golovin (1963) and with finite difference solutions of the two-component kinetic collection equation obtained for the Golovin (sum) and hydrodynamic kernels. Very good agreement was observed between the Monte Carlo simulations and the analytical and numerical solutions. A simulation for realistic initial conditions is presented for the hydrodynamic kernel. As expected, the aerosol mass is shifted from small to large particles due to collection process. This algorithm could be extended to incorporate various properties of clouds such several crystals habits, different types of soluble CCN, particle charging and drop breakup.

Simulating the evolution of soot mixing state with a particle‐resolved aerosol model

“… Babovsky [1999] and Eibeck and Wagner [2001] developed the Mass Flow Algorithm with variable computational/physical particle ratios, Kolodko and Sabelfeld [2003] gave relevant error estimates, and Debry et al [2003] coupled it to evaporation and condensation. Somewhat similarly, Laurenzi et al [2002] and Alfonso et al [2008] (on the basis of ideas from Spouge [1985]) stored the number of particles with identical composition to reduce memory usage and computational expense while using Gillespie's method. Guias [1997] studied convergence of stochastic coagulation to the Smolukowski equation.…”

The validity of the kinetic collection equation revisited – Part 2: Simulations for the hydrodynamic kernel

“…The numerical integration of Eq. (1) was performed using the Adams-Bashfort-Moulton predictorcorrector method (Alfonso et al, 2009). For the finite difference scheme, droplet mass in the numerical grid is expressed as multiples of the mass of the initial 14µm monomer droplet.…”

The validity of the kinetic collection equation revisited – Part 2: Simulations for the hydrodynamic kernel

“…The numerical integration of Eq. ( 1) was performed using the Adams-Bashfort-Moulton predictorcorrector method (Alfonso et al, 2009). For the finite difference scheme, droplet mass in the numerical grid is expressed Product Kernel: K(x,y)=Cxy (C=5.49 x 10 9 cm 3 g -2 s -1 ) Analytical solution (t=1000 sec) Numerical solution (t=1000 sec) Analytical Solution (t=1300 sec) Numerical Solution (t=1300 sec)…”