Nuclear aerosols can originate from severe core damage in light water reactors, core disruptive accidents in fast reactors, nuclear accidents during nuclear material transport, at waste disposal sites, or from explosions and can evolve under natural transport processes as well as under the influence of engineered safety features. Such aerosols can be hazardous for the equipment inside the reactor and when leaked to the environment pose potential risks to the public. However, the computation of aerosol evolution is complicated, and an exploration of the direct simulation Monte Carlo technique to elucidate the role of various physical phenomena that influence the evolution, and eventually to help develop a production computer program, has been undertaken. We have extended here the previous work in important new directions by including most coagulation mechanisms such as Brownian, gravitational, and turbulence. We have also explored the Metropolis algorithm for sampling particles. We have found that the Metropolis algorithm permits efficient simulation of a much larger number of particles because it does not require precomputation and periodic update of the collisional matrix after each collision, unlike the direct sampling method.