Propagation of pollutants in the atmosphere based on 3D Navier–Stokes equations: Direct and inverse source problem

Abstract The article presents a description of the methodology for three-dimensional modeling of the gaseous pollutants spread in the atmospheric air. The methodology is based on solving a complete hydrodynamic system of equations – the Reynolds-averaged Navier–Stokes equations together with the equations of concentration transfer based on the Fick diffusion law, in conjunction with the equations of the turbulence model. Such a technique will allow for accurate modeling of the transfer of gaseous pollutants, without taking into account empirical patterns. The advantages of such a technique include the ability to take into account the turbulence, terrain, wind rose, underlying surface and geometry of pollution sources, accounting for the compressibility of the medium and the ability to specify an accurate dependence of the stratification of atmospheric air. The article presents the results of numerical modeling of the test case of propane emission from a single source, as well as the problem of dispersion of mixed emissions from a single chimney and determination of the maximum ground concentration of harmful substances. The results of the modeling are evaluated, and compared with experimental data, using the method of calculating the maximum one-time concentrations from emissions of a single point source using the adopted empirical methodology. It is shown that the technique allows estimating all hydrodynamic parameters of polluted air distribution with the required accuracy. The empirical approach is used for the inverse source problem of determining the location of the emission source by known pollutant concentrations. We show a good localization of the source by global optimization method (differential evolution) and that this approximate solution of inverse problem can be considered as good initial guess for iterative methods to solve the inverse source pollutant problem based on the Navier–Stokes equations.