Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence
For researchers using numerical simulations of turbulent flows, this work identifies discretization choices that better preserve helicity, a key invariant, improving physical fidelity.
This work investigates how different numerical discretization methods (spectral and finite-differencing) and convective term formulations affect discrete helicity conservation in simulations of helical turbulence. The study shows that certain methods better preserve helicity, with implications for the accuracy of turbulent flow simulations.
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.