High Order Semi-Lagrangian Methods for the Incompressible Navier-Stokes Equations

We propose a class of semi-Lagrangian methods of high approximation order in space and time, based on spectral element space discretizations and exponential integrators of Runge-Kutta type. The methods were presented in [7] for simpler convection-diffusion equations. We discuss the extension of these methods to the Navier-Stokes equations, and their implementation using projections. SemiLagrangian methods up to order three are implemented and tested on various examples. The good performance of the methods for convection-dominated problems is demonstrated with numerical experiments.