  A numerical method for the two-dimensional, incompressible Navier--Stokes
equations in vorticity--streamfunction form is proposed, which employs
semi-Lagrangian discretizations for both the advection and diffusion terms,
thus achieving unconditional stability without the need to solve linear systems
beyond that required by the Poisson solver for the reconstruction of the
streamfunction. A description of the discretization of Dirichlet boundary
conditions for the semi-Lagrangian approach to diffusion terms is also
presented. Numerical experiments on classical benchmarks for incompressible
flow in simple geometries validate the proposed method.
