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Abstract: We demonstrate an approach to solving the coagulation equation that involvesusing a finite number of moments of the particle size distribution. Thisapproach is particularly useful when only general properties of thedistribution, and their time evolution, are needed. The numerical solution tothe integro-differential Smoluchowski coagulation equation at every time step,for every particle size, and at every spatial location is computationallyexpensive, and serves as the primary bottleneck in running evolutionary modelsover long periods of time. The advantage of using the moments method comes inthe computational time savings gained from only tracking the time rate ofchange of the moments, as opposed to tracking the entire mass histogram whichcan contain hundreds or thousands of bins depending on the desired accuracy.The collision kernels of the coagulation equation contain all the necessaryinformation about particle relative velocities, cross-sections, and stickingcoefficients. We show how arbitrary collision kernels may be treated. Wediscuss particle relative velocities in both turbulent and non-turbulentregimes. We present examples of this approach that utilize different collisionkernels and find good agreement between the moment solutions and the moments ascalculated from direct integration of the coagulation equation. As practicalapplications, we demonstrate how the moments method can be used to track theevolving opacity, and also indicate how one may incorporate porous particles.

Autor: Paul R. Estrada, Jeffrey N. Cuzzi



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