Large time-step explicit integration method for solving problems with dominant convection

Published in Computer Methods in Applied Mechanics and Engineering Vol. 217-220, pp. 168-185, 2012
doi: 10.1016/j.cma.2011.12.008

Abstract

An explicit time integrator without the CFL $<1$ restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated by convection, independently of the spatial discretization.

The idea is to use the information existing at time $t=t^{n}$ in the velocity streamlines as well as in the acceleration streamlines to update the particle position as well as the velocity in an updated Lagrangian frame. The method may be used with moving or fixed meshes.