A new velocity-vorticity boundary integral formulation for Navier-Stokes equations

摘要

In the present work, an indirect boundary integral method for the numerical solution of Navier-Stokes equations formulated in velocity-vorticity dependent variables is proposed. This wholly integral approach, based on Helmholtz's decomposition, deals directly with the vorticity field and gives emphasis to the establishment of appropriate boundary conditions for the vorticity transport equation. The coupling between the vorticity and the vortical velocity fields is expressed by an iterative procedure. The present analysis shows the usefulness of an integral formulation not only in providing a potentially more efficient computational tool, but also in giving a better understanding to the physics of the phenomenon.