A consistent boundary condition for vorticity–streamfunction simulation of wall-bounded vortex flow

This paper was motivated by a computational effort to model the aircraft wake vortex hazard near airports. Those flows can usually be approximated as a pair of two-dimensional, incompressible vortices interacting with an infinite solid wall. The present numerical model uses a vorticity–streamfunction formulation to simulate the two-dimensional problem. Since vorticity generation near the wall alters the evolution of the secondary and tertiary vortices directly, accurate modeling of the wall region is critical. A local relationship between vorticity and streamfunction for a wall boundary condition has been established from a new point of view, by specifying the streamfunction at the boundary grid lifted away from the solid wall. The new method has utilized Taylor series expansions near the wall boundary. Although the resulting expressions are only first order accurate, the critical importance of physical and mathematical consistency has been achieved. Numerical test cases are discussed in the paper.