Scale-selective dissipation in energy-conserving finite element schemes for two-dimensional turbulence
For computational fluid dynamics researchers, this work quantifies the multiscale properties of two specific discretizations, but the results are incremental and lack concrete performance numbers.
The paper analyzes energy-conserving finite element schemes for 2D turbulence, showing that they model scale interactions and reproduce non-local energy backscatter, with the Lie derivative method providing better enstrophy control.
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.