  Porosity evolution of dust aggregates is crucial in understanding dust
evolution in protoplanetary disks. In this study, we present useful tools to
study the coagulation and porosity evolution of dust aggregates. First, we
present a new numerical method for simulating dust coagulation and porosity
evolution as an extension of the conventional Smoluchowski equation. This
method follows the evolution of the mean porosity for each aggregate mass
simultaneously with the evolution of the mass distribution function. This
method reproduces the results of previous Monte Carlo simulations with much
less computational expense. Second, we propose a new collision model for porous
dust aggregates on the basis of our N-body experiments on aggregate collisions.
We first obtain empirical data on porosity changes between the classical limits
of ballistic cluster-cluster and particle-cluster aggregation. Using the data,
we construct a recipe for the porosity change due to general hit-and-stick
collisions as well as formulae for the aerodynamical and collisional cross
sections. Simple coagulation simulations using the extended Smoluchowski method
show that our collision model explains the fractal dimensions of porous
aggregates observed in a full N-body simulation and a laboratory experiment.
Besides, we discover that aggregates at the high-mass end of the distribution
can have a considerably small aerodynamical cross section per unit mass
compared with aggregates of lower masses. We point out an important implication
of this discovery for dust growth in protoplanetary disks.
