Solution of Smoluchowski coagulation equation for Brownian motion with TEMOM

The particle number density in the Smoluchowski coagulation equation usually cannot be solved as a whole,and it can be decomposed into the following two functions by similarity transformation:one is a function of time(the particle k-th moments),and the other is a function of dimensionless volume(self-preserving size distribution).In this paper,a simple iterative direct numerical simulation(iDNS)is proposed to obtain the similarity solution of the Smoluchowski coagulation equation for Brownian motion from the asymptotic solution of the k-th order moment,which has been solved with the Taylor-series expansion method of moment(TEMOM)in our previous work.The convergence and accuracy of the numerical method are first verified by comparison with previous results about Brownian coagulation in the literature,and then the method is extended to the field of Brownian agglomeration over the entire size range.The results show that the difference between the lognormal function and the self-preserving size distribution is significant.Moreover,the thermodynamic constraint of the algebraic mean volume is also investigated.In short,the asymptotic solution of the TEMOM and the self-preserving size distribution form a one-to-one mapping relationship;thus,a complete method to solve the Smoluchowski coagulation equation asymptotically is established.