A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation

Abstract

This work focuses on the Parareal parallelin-time method and its application to the viscous Burgers equation. A crucial component of Parareal is the coarse time stepping scheme, which strongly impacts the convergence of the parallel-in-time method. Three choices of coarse time stepping schemes are investigated in this work: explicit Runge-Kutta, implicit-explicit Runge-Kutta, and implicit Runge-Kutta with semiLagrangian advection. Manufactured solutions are used to conduct studies, which provide insight into the viability of each considered time stepping method for the coarse time step of Parareal. One of our main findings is the advantageous convergence behavior of the semi-Lagrangian scheme for advective flows.