A MEEVC discretization for two-dimensional incompressible Navier-Stokes equations with general boundary conditions

TL;DR

This paper presents a new mixed finite element discretization method for 2D incompressible Navier-Stokes equations that conserves key physical quantities and can handle no-slip boundary conditions, with proven conservation properties and numerical validation.

Contribution

It introduces a mass, energy, enstrophy, and vorticity conserving discretization that extends previous schemes to include no-slip boundary conditions.

Findings

Conservation of physical quantities is proven.

Numerical experiments validate the method.

Supports exact and inexact quadrature.

Abstract

In this work, we introduce a mass, energy, enstrophy and vorticity conserving (MEEVC) mixed finite element discretization for two-dimensional incompressible Navier-Stokes equations as an alternative to the original MEEVC scheme proposed in [A. Palha and M. Gerritsma, J. Comput. Phys., 2017]. The present method can incorporate no-slip boundary conditions. Conservation properties are proven. Supportive numerical experiments with both exact and inexact quadrature are provided.