Viscous flow simulation of a two-dimensional channel flow with complex geometry using the grid-particle vortex method

Abstract
To avoid a large consumption of computer time instead of the direct vortex methods with Biot-Savart interaction law, the vortex in cell method was used. The local velocity of a particle was obtained by the solution of the Poisson equation for the stream function, its differentiation, and then interpolation of velocity to the vortex particle position from the grid nodes. 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.