Simulation of a Pollutant Transport in an Atmosphere With Shock Waves

In this work a model for transport phenomena in an environment representing the atmosphere containing a pollutant is presented by considering mass and linear momentum conservation for the air-pollutant mixture as well as the mass balance for the pollutant. The resulting mathematical description consists of a nonlinear system of hyperbolic equations that admits discontinuities in addition to smooth or classical solutions. The Riemann problem associated with a class of problems describing the transport of a pollutant in an ideal gas with constant temperature with a discontinuous mass density distribution as initial condition is discussed. Numerical approximations for this nonlinear system in which the problem is solved subjected to a discontinuous initial condition — a jump, originating, in most cases, shock waves — are obtained by employing Glimm’s method and considered in some numerical simulations.