On the Analysis of the Second Order Time Filtered Backward Euler Method for the EMAC formulation of Navier-Stokes Equations

TL;DR

This paper introduces a second-order, unconditionally stable time filtering method for the EMAC formulation of Navier-Stokes equations, enhancing accuracy while conserving physical quantities.

Contribution

It develops a modular second-order time filtering technique for backward Euler applied to EMAC Navier-Stokes, improving solution accuracy without sacrificing conservation properties.

Findings

The filtered method is unconditionally stable.

It significantly improves numerical accuracy.

Conserves energy, momentum, and angular momentum.

Abstract

This paper considers the backward Euler based linear time filtering method for the EMAC formulation of the incompressible Navier-Stokes equations. The time filtering is added as a modular step to the standard backward Euler code leading to a 2-step, unconditionally stable, second order linear method. Despite its success in conserving important physical quantities when the divergence constraint is only weakly enforced, the EMAC formulation is unable to improve solutions of backward Euler discretized NSE. The combination of the time filtering with the backward Euler discretized EMAC formulation of NSE greatly increases numerical accuracy of solutions and still conserves energy, momentum and angular momentum as EMAC does. Several numerical experiments are provided that both verify the theoretical fidings and demonstrate superiority of the proposed method over the unfiltered case.