Scale-selective dissipation in energy-conserving finite element schemes for two-dimensional turbulence

TL;DR

This paper investigates how energy-conserving finite element schemes for 2D turbulence manage multiscale interactions and enstrophy control, focusing on their ability to replicate non-local energy backscatter in turbulent flows.

Contribution

It analyzes the multiscale properties of specific energy-conserving finite element discretizations, highlighting their effectiveness in modeling scale interactions and energy backscatter.

Findings

Schemes effectively control enstrophy and model scale interactions.

Discretizations reproduce non-local energy backscatter in turbulence.

Performance varies between Lie derivative and SUPG methods.

Abstract

We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretisation introduced in Natale and Cotter (2016a) and the Streamline Upwind/Petrov-Galerkin (SUPG) discretisation of the vorticity advection equation. Such discretisations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non-local energy backscatter that characterises two-dimensional turbulent flows.