Piecewise Polynomial Solutions of Aerosol Dynamic Equation

This paper presents a discretization technique for particle dynamics equation based on piecewise continuous approximations of the solution. The growth terms are re-solved using a Discontinuous Galerkin approach, and the coagulation by a collocation approach. The method fits in the general framework recently proposed by the author. The discontinuous approximation allows better representations of distributions with sharp peaks. Numerical tests reveal that accurate solutions can be obtained with a very small number of size bins. An efficient software package AeroSolve which implements the proposed algorithms was developed.

Acknowledgments

This work was supported by NSF through CAREER award ACI-0413872 and NSF ITR award AP&IM 0205198. Part of the implementation originates from the M.S. thesis work of C. Borden at Michigan Technological University. The author thanks M. Z. Jacobson for providing the original implementation of the semi-implicit method.