AeroSolve: A Solver Package for the Aerosol Dynamic Equations

Adrian Sandu (sandu@cs.vt.edu)

Summary


AeroSolve is a package to obtain numerical solutions of the integro-differential particle dynamic equation. The particle distribution is approximate by piecewise polynomials, the discretization of the growth term is based on the discontinuous Galerkin approach, while the discretization of the coagulation term uses a collocation approach. Approximations with piecewise polynomials of order 0 through 3 are implemented.

AeroSolve alows accurate solutions with a very small number of size bins.

AeroSolve was developed with support from NSF through the CAREER award ACI-0093139 and  ITR award AP&IM 0205198.

Part of the implementation was performed by Christian T. Borden as part of his the M.S. thesis work at Michigan Technological University.


Licence

The software is freely distributed under the provisions of GNU General Public Licence. By downloading the software you aggree to cite the following article in any work that uses the software: A. Sandu, "Piecewise polynomial solutions of aerosol dynamic equations", Computer Science technical report CS-TR-04-01, Virginia Polytechnic Institute and State University, Jan. 2004.


Download

The source code (tar.gz or zip file) can be downloaded after aggreeing with the above.


Overview

As our understanding expands, new processes  are incorporated into air quality computer models. One example is the particulate matter (aerosol) processes, the importance of which is now widely recognized.  Aerosols are now a priority focus area in environmental science  due to the leading role they play as a cause of adverse human health,  and their ability to scatter and absorb incoming solar radiation  and thus modify warming due to greenhouse gases and reduce visibility.  Particulate matter (aerosol) processes are ``emerging as a new frontier'' in environmental studies (Nobel laureate P. Crutzen, 1998).

To accurately study the effects of aerosols it is necessary to resolve aerosol number and mass distributions as a function of chemical composition and size. The evolution of particle number (or mass concentration) distribution in time is governed by an integro-differential equation, called the particle dynamics equation.  Aerosolve is a package to obtain numerical solutions of the particle dynamics equation. The distribution is approximate by piecewise polynomials. The discretization of growth is done with a discontinuous Galerkin approach, while the discretization of coagulation is done using a collocation approach.


Results

AeroSolve computes very accurate solutions with a small number of size bins. Examples are shown below.

1) The exact and numerical solutions obtained by AEROSOLVE for 48 hours of coagulation and growth of an initial population with exponential number density. All numerical solutions use 12 degrees of freedom, but for different approximation degrees.


2) The evolution of numerical errors with the number of degrees of freedom for the same test problem, different approximation orders.