This paper is aimed at creating and realization of new physical model of impurity transfer (solid particles and heavy gases) in areas with non-flat and/or non-stationary boundaries. The problem in hand is principally divided into two sub-problems: describing of atmosphere stream in the planetary boundary layer under non-homogeneous and/or non-stationary conditions, and prediction of spatial-temporal distribution of impurity transferred by a stream. Well-known traditional boundary layer theories are applicable to atmosphere flows along flat, homogeneous and stationary surfaces. Along such an ideal surface boundary layer is also horizontally homogeneous and equilibrium. The problem of particulate distribution in these simple cases is reduced to resolving of passive scalar equations for turbulent flow in boundary layer. In case when concentration of impurity or external factors are beyond of range of applicability of passive scalar approach, the full set of thermo-hydrodynamic equations of boundary layer using sub-grid scale turbulent flow parameterization in large eddy simulations method or in Reynolds averaged equations is used. The method developed is aimed to overcome difficulties of traditional models above discussed. Our model allows to analyze phenomena due to complex topology of flow over obstacles and to describe processes at an interface of solid particles cloud and pure atmosphere. As initial equation we use Nigmatulin ones which describe two-phase fluid by perfect gas equation with recalculated state equation.

The main idea of suggested method is to use non-viscous equations for solid particles transport modeling in the vicinity of complex boundary. In viscous atmosphere the non-slip boundary condition on solid surface must be observed. This postulates the reduction of velocity to zero at a solid surface. For conditions considered essential changes of hydrodynamic fields near solid boundary caused not only by non-slip condition but also by a various relief of surface: mountains, street canyons, individual buildings. Transport of solid particles, their ascent and precipitation also result in dramatic changes of meteorological fields. As dynamic processes of solid particles transfer accompanying the flow past of complex relief surface by wind flows is of our main interest we are to use equations of non-viscous hydrodynamic. We should put up with on the one hand idea of big wind gradients in the boundary layer and on the other hand disregard of molecular viscosity in two-phase atmosphere equations. We deal with describing big field gradients with the aid of scheme viscosity of numerical algorithm used to model near-surface phenomena.

In present paper is shown that the presence of two scheme viscosity mechanisms, namely presence of non-homogeneous surface and solid impurity concentration gradients allows reproducing particulate transport dynamics. Adduced 2D numerical calculations for three types of obstacles (rectangular canyon, rectangular and triangular brows) demonstrate effectiveness of the model to reproduce complicated flow topology, namely deattached flow zones, recircullated flow zones and backflow zones.