DNS and role of round-off error: Two-Dimensional Taylor-Green vortex problem

TL;DR

This study demonstrates that round-off errors significantly influence the receptivity and instability of fluid flows in the 2D Taylor-Green vortex problem, with high-precision simulations revealing new flow behaviors.

Contribution

It is the first to conclusively establish the impact of round-off errors on flow receptivity and instability using high-accuracy simulations with different precisions.

Findings

Quadruple precision alters the flow's receptivity route to turbulence.

Identification of a previously unreported receptivity phase.

Round-off errors have a critical role in flow stability and decay.

Abstract

The role of round-off errors on the receptivity and instability of fluid flows are conclusively established for the first time using high accuracy simulations of the benchmark two-dimensional (2D) Taylor-Green vortex problem using double and quadruple precisions. Employing the fourth order Runge-Kutta (RK4) method for temporal discretization and Fourier pseudospectral method for spatial discretization enables unprecedented accuracy necessary for controlling all forms of errors, except the remaining round-off error. Results clearly show that adopting quadruple precision results in a qualitatively different receptivity route to turbulence and its subsequent decay compared to double precision. Another important observation is the identification of the receptivity phase which has never been reported before. Present study not only establishes the singular role of round-off errors but also has potential ramifications on receptivity and instability of flows due to precision of simulation.