Structure preserving finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility

TL;DR

This paper introduces two new finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility, ensuring conservation, energy stability, and approximate maximum principle preservation, supported by numerical validation.

Contribution

The paper develops and analyzes two novel numerical schemes that are conservative, energy-stable, and handle degenerate mobility in the Navier-Stokes-Cahn-Hilliard system.

Findings

Schemes are conservative and energy-stable.

Numerical results confirm accuracy and stability.

Comparison shows differences with constant mobility models.

Abstract

In this work we present two new numerical schemes to approximate the Navier-Stokes-Cahn-Hilliard system with degenerate mobility using finite differences in time and finite elements in space. The proposed schemes are conservative, energy-stable and preserve the maximum principle approximately (the amount of the phase variable being outside of the interval [0,1] goes to zero in terms of a truncation parameter). Additionally, we present several numerical results to illustrate the accuracy and the well behavior of the proposed schemes, as well as a comparison with the behavior of the Navier-Stokes-Cahn-Hilliard model with constant mobility.