An energy, momentum and angular momentum conserving scheme for a regularization model of incompressible flow

TL;DR

This paper presents EMAC-Reg, a new regularization of the EMAC formulation for incompressible flow that conserves key physical quantities and is suitable for coarser mesh computations, demonstrated through theoretical analysis and numerical results.

Contribution

The paper introduces EMAC-Reg, a regularized EMAC model that conserves energy, momentum, and angular momentum, and is well-posed and accurate for coarse mesh simulations.

Findings

EMAC-Reg conserves energy, momentum, and angular momentum.

The model is well-posed and achieves optimal accuracy.

Numerical results confirm robustness on coarse meshes.

Abstract

We introduce a new regularization model for incompressible fluid flow, which is a regularization of the EMAC formulation of the Navier-Stokes equations (NSE) that we call EMAC-Reg. The EMAC (energy, momentum, and angular momentum conserving) formulation has proved to be a useful formulation because it conserves energy, momentum and angular momentum even when the divergence constraint is only weakly enforced. However it is still a NSE formulation and so cannot resolve higher Reynolds number flows without very fine meshes. By carefully introducing regularization into the EMAC formulation, we create a model more suitable for coarser mesh computations but that still conserves the same quantities as EMAC, i.e., energy, momentum, and angular momentum. We show that EMAC-Reg, when semi-discretized with a finite element spatial discretization is well-posed and optimally accurate. Numerical results are provided that show EMAC-Reg is a robust coarse mesh model.