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The paper deals with a mathematical and numerical study of the Atmospheric Boundary Layer (ABL) flow over a complex topography represented either by part of the Giant mountains or by a surface brown coal mine and a coal depot, both located in the North Bohemia. Various types of protective obstacles have been tested and compared, mainly with respect to the reduction of dustiness in the latter case. The mathematical model is based on system of Reynolds Averaged Navier-Stokes (RANS) equations for viscous and incompressible flow. The artificial compressibility method was used. The numerical method is based either on the finite-volume explicit scheme or on a semi-implicit finite-difference scheme. A simple algebraic turbulence model is applied to close the governing system of equations. Moreover, an additional transport equation for a passive pollutant has been considered. [ABSTRACT FROM AUTHOR]

Diffusion equations in multicomponent environments, as parabolic evolutionary systems, have many physical and engineering applications; another their application was accentuated in 2020 due to the Covid19 infection. This short paper demonstrates the possibility of numerical analysis of direct and inverse problems of this type using some algorithms from computational heat, mass, etc. transfer, with special nonlinear terms originated in mathematical biology. One simple example sketches the benefits and hazards of such prediction for the MATLAB-based analysis of readily available Covid19 spread data from the Czech Republic. [ABSTRACT FROM AUTHOR]