A velocity decomposition formulation for 2D steady incompressible lifting problems

The principle of velocity decomposition is used to efficiently and accurately solve the Navier-Stokes boundary-value problem for lifting flows. The velocity vector is decomposed as the sum of irrotational and vortical components. The irrotational component is represented using a velocity potential which satisfies the Laplace equation with a modified boundary condition that is written in terms of the Navier-Stokes solution. A viscous potential can be found which satisfies the Navier-Stokes problem directly outside of the rotational regions of the fluid such that the fluid domain over which the Navier-Stokes equations must be solved numerically can be greatly reduced. The viscous potential is used as a Dirichlet boundary condition for the total velocity on the boundaries of the reduced fluid domain. The velocity decomposition approach is used to solve for the flow over a 2D NACA0012 foil in both laminar and turbulent regimes.