Finite Volume Modelling of Free Surface Draining Vortices

A numerical solution of free-surface vortex forming field based on an axial-symmetric finite volume model has been developed for solving the incompressible Navier-Stokes equations on irregular geometries. Boundary conditions include Dirichlet and Neumann type while the mesh is staggered. The numerical scheme is a semi-implicit, where the terms controlling the diffusion and those controlling the pressure field are discretized implicitly, while the convective terms are approximated via an Euler-Lagrange approach. The discrete version of the continuity equation becomes, by a substitution, a system having the pressure values as the only unknowns.