Glimm’s method simulation for the pollutant transport in an isothermal atmosphere

In this work, a model for the transport of a pollutant in the atmosphere 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 and discontinuous distribution for either mass density or velocity or pollutant concentration as initial condition is carefully discussed. Numerical approximations for this nonlinear system are obtained by employing Glimm’s method and considered in some numerical simulations.