A new approach is suggested for numerical simulation of transport processes in highly nonequilibrium conditions at the microscopic level using a technique of the self-consistent nonlocal hydrodynamical equations. The approach allows to generalize and match the known results as well as to describe the new effects that can not occur in the continuous media conceptions. Some explicit solutions of the admixture stationary diffusion problem in the rarefied background gas flow in a long tube with absorbing walls are obtained which describe longitudinal admixture relaxation and concentration distribution by the tube cross-section and are not solutions of the usual diffusion equation.