Parareal convergence for 2D unsteady flow around a cylinder

TL;DR

This paper investigates the convergence behavior of the Parareal algorithm applied to 2D unsteady flow around a cylinder, comparing implicit Euler and fractional step methods across viscosities, highlighting the impact of numerical diffusion.

Contribution

It provides new insights into how different fine integrators affect Parareal convergence in fluid flow simulations, emphasizing the role of numerical diffusion.

Findings

Parareal converges better with implicit Euler due to numerical diffusion.

Convergence depends on the choice of fine integrator and viscosity.

Implicit Euler under-resolves fine-scale dynamics, improving convergence.

Abstract

In this technical report we study the convergence of Parareal for 2D incompressible flow around a cylinder for different viscosities. Two methods are used as fine integrator: backward Euler and a fractional step method. It is found that Parareal converges better for the implicit Euler, likely because it under-resolves the fine-scale dynamics as a result of numerical diffusion.