  State-of-the-art models for aerosol particle nucleation and growth from a
cooling vapor primarily use a nodal method to numerically solve particle growth
kinetics. In this method, particles that are smaller than the critical size are
omitted from consideration, because they are thermodynamically unfavorable.
This omission is based on the assumption that most of the newly formed
particles are above the critical size and that the subcritical-size particles
are not important to take into account. Due to the nature of the nodal method,
it suffers from the numerical diffusion, which can cause an artificial
broadening of the cluster size distribution leading to significant
overestimation of the number of large-size particles. To address these issues,
we propose a more accurate numerical method that explicitly models particles of
all sizes, and uses a special numerical scheme that eliminates the numerical
diffusion. We extensively compare this novel method to the commonly used nodal
solver of the General Dynamics Equation (GDE) for particle growth and
demonstrate that it offers GDE solutions with higher accuracy without
generating numerical diffusion. Incorporating small subcritical clusters into
the solution is crucial for: 1) more precise determination of the entire shape
of the particle size distribution function and 2) wider applicability of the
model to experimental studies with non-monotonic temperature variations leading
to particle evaporation. The computational code implementing this numerical
method in Python is available upon request.
