Robust and Efficient Modular Grad-Div Stabilization

TL;DR

This paper introduces two modular grad-div stabilization algorithms for Navier-Stokes equations that are stable, efficient, and easy to integrate, with proven convergence and demonstrated numerical benefits.

Contribution

The paper develops minimally intrusive, stable, and convergent modular grad-div algorithms that outperform fully coupled methods in efficiency and robustness.

Findings

Algorithms are stable and optimally convergent.

Numerical tests confirm improved efficiency over fully coupled methods.

Methods do not suffer from locking or slowdowns at large grad-div parameters.

Abstract

This paper presents two modular grad-div algorithms for calculating solutions to the Navier-Stokes equations (NSE). These algorithms add to an NSE code a minimally intrusive module that implements grad-div stabilization. The algorithms do not suffer from either breakdown (locking) or debilitating slow down for large values of grad-div parameters. Stability and optimal-order convergence of the methods are proven. Numerical tests confirm the theory and illustrate the benefits of these algorithms over a fully coupled grad-div stabilization.