Exponential time integrators for unsteady advection-diffusion problems on refined meshes

TL;DR

This paper investigates exponential time integrators as an efficient alternative for solving unsteady advection-diffusion problems on refined meshes, addressing challenges posed by local mesh refinement and advection terms.

Contribution

The study compares three exponential integrators with the Rosenbrock ROS2 method, demonstrating their effectiveness for advection-diffusion problems on refined meshes.

Findings

Exponential integrators handle local mesh refinement efficiently.

Compared to Rosenbrock ROS2, exponential methods show competitive performance.

Exponential methods are simple and effective for advection-dominated problems.

Abstract

Time integration of advection dominated advection-diffusion problems on refined meshes can be a challenging task, since local refinement can lead to a severe time step restriction, whereas standard implicit time stepping is usually hardly suitable for treating advection terms. We show that exponential time integrators can be an efficient, yet conceptually simple, option in this case. Our comparison includes three exponential integrators and one conventional scheme, the two-stage Rosenbrock method ROS2 which has been a popular alternative to splitting methods for solving advection-diffusion problems.