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A numerical method for the two-dimensional, incompressible Navier--Stokesequations in vorticity--streamfunction form is proposed, which employssemi-Lagrangian discretizations for both the advection and diffusion terms,thus achieving unconditional stability without the need to solve linear systemsbeyond that required by the Poisson solver for the reconstruction of thestreamfunction. A description of the discretization of Dirichlet boundaryconditions for the semi-Lagrangian approach to diffusion terms is alsopresented. Numerical experiments on classical benchmarks for incompressibleflow in simple geometries validate the proposed method.

A fully semi-Lagrangian discretization for the 2D Navier--Stokes equations in the vorticity--streamfunction formulation