Glimm Scheme and Operator Splitting for Simulating Radial Transport of a Pollutant in an Atmosphere

Abstract

Aiming to describe transport phenomena in an atmosphere containing a pollutant, assuming radial transport of the pollutant and the atmosphere as an ideal isothermal gas, this work yields a nonlinear hyperbolic system of three partial differential equations that represent mass and momentum conservation for the air-pollutant mixture and the pollutant mass balance. The hyperbolic nature of the system demands a numerical method capable of handling discontinuities. In this context, Glimm's scheme is naturally chosen for the numerical simulation, combined with an operator-splitting technique to account for the non-homogeneous portion of the operator, arising naturally from the problem's spherical geometry.