Chorin-Marsden product formula [9], besides factoring the convective and the diffusive components of the Navier-Vortex methods, based on the splitting into Euler and Stokes operators, have been successfully adopted in numerical solutions Stokes equations, considers a creation operator to introof three-dimensional Navier-Stokes equations in free-space. Here duce the concentrated vorticity layer at the wall which is we deal with their application to flows bounded by solid walls, successively diffused into the flow field. Afterwards, Bendiscussing in particular the boundary conditions for vorticity and fatto and Pulvirenti provided a rigorous mathematical basis their approximation. In two dimensions this has been accomplished for this procedure. In particular in a first paper [6], they by introducing a vortex sheet at the wall, determined by the local slip-velocity, as an approximation of the vorticity source. For threeintroduced the concept of a vorticity source at the wall, dimensional flows, we analyze in the context of the Stokes substep whose intensity is to be determined by solving a suitable the integral equation for the vorticity source and its connection with integral equation. The integral equation reflects the nonlothe creation algorithm adopted in vortex methods. The present cal nature of the boundary condition for a vorticity formuanalysis leads to a formulation which shows the connection between the exact vorticity source at the wall and the discrete vorticity lation, as clearly pointed out by Quartapelle [16] in the creation operator adopted in the Chorin-Marsden formula. In particcontext of a different numerical approach. In a successive ular, the slip velocity at the wall is identified as an approximate paper [7] they show how, after introducing the local operasolution of the integral equation for the vorticity source and the tor for the vorticity creation at the wall, the algorithm is corresponding error estimate is also discussed. Besides showing convergent to the Navier-Stokes solution, obtained with the consistency of this approximation, we indicate a numerical procedure which provides a wall-generation of solenoidal vorticity. This the exact vorticity source. is a crucial issue for an accurate application of vortex methods to
In the present paper we study the generation by solid three-dimensional flows.