Property-preserving numerical approximation of a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility

TL;DR

This paper introduces a novel finite element and discontinuous Galerkin based numerical scheme for simulating a complex fluid model that maintains physical properties like mass, density bounds, and energy decay.

Contribution

It develops a new computational framework that preserves key physical properties for a variable density Cahn-Hilliard-Navier-Stokes model with degenerate mobility.

Findings

The scheme successfully preserves mass, density bounds, and energy decay.

Numerical experiments demonstrate convergence and effectiveness on benchmark problems.

The approach offers a reliable tool for simulating complex fluid interactions.

Abstract

In this paper, we present a new computational framework to approximate a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility that preserves the mass of the mixture, the pointwise bounds of the density and the decreasing energy. This numerical scheme is based on a finite element approximation for the Navier-Stokes fluid flow with discontinuous pressure and an upwind discontinuous Galerkin scheme for the Cahn-Hilliard part. Finally, several numerical experiments such as a convergence test and some well-known benchmark problems are conducted.