Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

TL;DR

This paper examines how different numerical methods affect the conservation of helicity in simulations of helical turbulence, highlighting the importance of discretization choices on physical invariants.

Contribution

It provides a theoretical and numerical analysis of how spectral and finite-difference methods preserve or violate helicity conservation in turbulent flow simulations.

Findings

Spectral methods better conserve helicity than finite-difference methods.

Discretization form significantly impacts helicity and energy transfer accuracy.

Runge-Kutta schemes influence the conservation properties in simulations.

Abstract

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an in-viscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space-and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations.