دانلود رایگان مقاله مدل سازی گرد و غبار انعقاد دانه

ABSTRACT

In molecular clouds, stars are formed from a mixture of gas, plasma and dust particles. The dynamics of this formation is still actively investigated and a study of dust coagulation can help to shed light on this process. Starting from a pre-existing discrete coagulation model, this work aims to mathematically explore its properties and its suitability for numerical validation. The crucial step is in our reinterpretation from its original discrete to a well-defined continuous form, which results in the well-known Smoluchowski coagulation equation. This opens up the possibility of exploiting previous results in order to prove the existence and uniqueness of a mass conserving solution for the evolution of dust grain size distribution. Ultimately, to allow for a more flexible numerical implementation, the problem is rewritten as a nonlinear hyperbolic integro-differential equation and solved using a finite volume discretisation. It is demonstrated that there is an exact numerical agreement with the initial discrete model, with improved accuracy. This is of interest for further work on dynamically coupled gas with dust simulations.

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.