A Vortex-In-Cell Method for the Simulation of Viscous Flows

A numerical technique of solving incompressible, vortex-dominated flows is described. The Navier-Stokes equations in velocity-vorticity formulation are integrated by a fractional step algorithm which treats convective motions and diffusive phenomena separately. Convection of vorticity is treated in a Lagrangian fashion, whereas the vorticity diffusion is computed on a grid by finite differences. The two problems are solved and combined at each time-step. The technique is as simple and robust as classical finite difference methods. Although being a bit more dissipative, it still preserves the spectral accuracy of fully Lagrangian vortex methods. The numerical procedure is validated against theoretical, experimental and numerical data from literature.