Semi-Lagrangian exponential integrators for the incompressible Navier-Stokes equations

preprint numerics no. 7/2011 norwegian university of science and technology trondheim, norway Direct applications of high order DIRK-CF methods as presented in [7] to the incompressible Navier-Stokes equations were found to yield a loss in order of convergence. The DIRK-CF methods are exponential integrators arising from the IMEX Runge-Kutta techniques proposed in [1], and are semi-Lagrangian when applied to convection diffusion equations. As discussed in [17], inappropriate implementation of projection methods for incompressible flows can lead to a loss in the order of convergence. In this paper we recover the full order of the IMEX methods using projections unto the space of divergence-free vector fields and we discuss the difficulties encountered in using similar techniques for the semi-Lagrangian DIRK-CF methods. We finally assess the performance of the semi-Lagrangian DIRK-CF methods for the Navier-Stokes equations in convection dominated problems.