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

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 recon- struction of the streamfunction. A description of the discretization of Dirichlet boundary conditions for the semi-Lagrangian approach to diffusion terms is also presented. Numeri- cal experiments on classical benchmarks for incompressible flow in simple geometries val- idate the proposed method.