A Micro-Macro parallel-in-time Implementation for the 2D Navier-Stokes Equations

TL;DR

This paper adapts the Micro-Macro Parareal parallel-in-time algorithm to 2D Navier-Stokes equations, demonstrating potential for reduced wall-time in simulating laminar flows around a cylinder with increasing Reynolds numbers.

Contribution

It introduces a parallel-in-time implementation for 2D Navier-Stokes equations using the Micro-Macro Parareal algorithm, tested on a cylinder flow benchmark with analysis of convergence behavior.

Findings

Achieved wall-time reduction compared to serial computation.

Convergence depends on Reynolds number and interpolation schemes.

Successfully approximated local states and lift coefficient in laminar flow.

Abstract

In this paper the Micro-Macro Parareal algorithm was adapted to PDEs. The parallel-in-time approach requires two meshes of different spatial resolution in order to compute approximations in an iterative way to a predefined reference solution. When fast convergence in few iterations can be accomplished the algorithm is able to generate wall-time reduction in comparison to the serial computation. We chose the laminar flow around a cylinder benchmark on 2-dimensional domain which was simulated with the open-source software OpenFoam. The numerical experiments presented in this work aim to approximate states local in time and space and the diagnostic lift coefficient. The Reynolds number is gradually increased from 100 to 1,000, before the transition to turbulent flows sets in. After the results are presented the convergence behavior is discussed with respect to the Reynolds number and the applied interpolation schemes.