Application of the votex-in-cell method for the simulation of two-dimensional viscous flow

In the paper the vortex in cell method for the simulation of the viscous flow in a complex geometry was described. Vorticity field is approximated by the collection of the particles that carries the circulation. The local velocity of a particle was obtained by the solution of the Poisson equation for the stream function by the grid method and then interpolation of velocity from the grid nodes to the vortex particle position. The Poisson equation for the stream function was solved by fast elliptic solvers. To be able to solve the Poisson equation in a region with a complex geometry, the capacitance matrix technique was used. The viscosity of the fluid was taken in a stochastic manner. A suitable stochastic differential equation was solved by the Huen method. The non-slip condition on the wall was realized by the generation of the vorticity. The program was tested by solving several flows in the channels with a different geometry and at a different Reynolds number. Here we present the testing results concerning the flow in a channel with sudden symmetric expansion, for the flow in channel with backward step, and the flow over building systems.