Structure-preserving approximation for the non-isothermal Cahn-Hilliard-Navier-Stokes system

TL;DR

This paper introduces a structure-preserving finite element approximation for the non-isothermal Cahn-Hilliard-Navier-Stokes system, ensuring the physical properties are maintained during numerical simulation.

Contribution

It presents a novel reformulation and discretization approach that preserves the system's structure using conforming finite elements and implicit time stepping.

Findings

The method maintains energy stability.

It accurately captures phase separation dynamics.

The approach is validated through numerical experiments.

Abstract

In this work we propose and analyse a structure-preserving approximation of the non-isothermal Cahn-Hilliard-Navier-Stokes system using conforming finite elements in space and implicit time discretisation with convex-concave splitting. The system is first reformulated into a variational form which reveal the structure of the equations, which is then used in the subsequent approximation.