8. Conclusions
The equivalence between the discrete coagulation model and the Smoluchowski continuous formulation has been proved and the kernel identified. With the specific kernel and initial condition it was possible to analytically infer existence of a unique, mass conserving solution. The continuous model, rewritten in the conservative form, allowed the use of a finite-volume discretisation, and both numerical approaches were demonstrated to produce mass conserving evolutions. Numerical properties such as convergence in the temporal as well as in the grain size bin discretisation were analysed. For the latter, it was shown that even a fairly coarse bin size distribution can yield satisfactory results of coagulation processes when the conservative formulation is used. This is of interest for future work, where we target spatio-temporally evolving gas–dust mixtures in molecular cloud contexts. All the different reformulations for the coagulation model are gathered in Table 3. Besides dynamic coupling through dragforces as was done to date, the present work paves the way to create a method that also accounts for coagulation processes in the dust distribution, thereby extending work like Birnstiel et al. (2010) to full 3D dynamical computations.
