A Fully Semi-Lagrangian Method for the Navier–Stokes Equations in Primitive Variables

We propose a semi-Lagrangian method for the numerical solution of the incompressible Navier–Stokes equations. The method is based on the Chorin–Temam fractional step projection method, combined with a fully semi-Lagrangian scheme to approximate both advective and diffusive terms in the momentum equation. A standard finite element method is used instead to solve the Poisson equation for the pressure. The proposed method allows to employ large time steps, while avoiding the solution of large linear systems to compute the velocity components, which would be required by a semi-implicit approach. We report numerical results obtained in two dimensions using triangular meshes on classical benchmarks, showing good agreement with reference solutions in spite of the very large time step employed.