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

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.

References in corpus (2)

• Compatible finite element spaces for geophysical fluid dynamics
• A variational H(div) finite element discretisation approach for perfect incompressible fluids

Cited by in corpus (3)

• Energy-enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions
• Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations
• Selective decay for the rotating shallow-water equations with a structure-preserving discretization