Adaptive Two-Step Peer Methods for Incompressible Navier–Stokes Equations

Abstract

The paper presents a numerical study of two-step peer methods up to order six, applied to the non-stationary incompressible Navier–Stokes equations. These linearly implicit methods show good stability properties, but the main advantage over one-step methods lies in the fact that even for PDEs no order reduction is observed. To investigate whether the higher order of convergence of the two-step peer methods equipped with variable time steps pays off in practically relevant CFD computations, we consider typical benchmark problems. Higher accuracy and better efficiency of the two-step peer methods compared to classical third-order one-step methods of Rosenbrock-type can be observed.