An AK-iDNS framework to solve the condensation-driven aggregation with realistic kernels

Abstract

In this study, a concise and fast framework based on the average kernel and iterative direct numerical simulation is proposed to solve the generalized Smoluchowski coagulation equation with a physically realistic kernel. Taking advantage of the symmetry of the homogeneous collision kernel, the realistic kernel function can be represented as a simple power function through Laplace transformation under the average kernel method, and the corresponding moment model and self-preserving model can then be constructed and solved analytically. Compared with the classical Taylor-series expansion method of moments, the present moment model has the same asymptotic growth rate, but the form is more concise and the particle number density is decoupled from the other moments. To obtain a better agreement with the experimental data, the iterative direct numerical simulation can be employed to correct the similarity solution using the analytical similarity solution as the initial condition. The corrected similarity solution overcomes the inherent contradiction between the analytical solution and experimental data discussed in the literature. The results reveal that the shape of self-preserving distribution is independent of the initial distribution and that it does depend on the mechanism of coagulation. The results also show the universality, reliability, and strong robustness of the iterative direct numerical simulation algorithm.