(untitled) (Archives of Mechanics - Test, 1997)
The random vortex method for two-dimensional, nonstationary flows of a viscous liquid in a spatially periodic, infinite system of airfoils is considered. The main idea is to approximate the evolution of the vorticity by a large set of small "vortex particles" (vortex blobs), which are transported in the velocity field (convection) and perform random walks according to Wiener process with standard deviation depending on the viscosity (diffusion). The velocity field is due to the induction of vortex blobs and includes also certain potential components. Since the flow domain is not simply connected, additional constraints concerning the vorticity production on the boundaries are introduced. They are necessary to obtain a solution with physically correct, single-valued pressure field. The results of numerical calculations are also presented.