Comparison of Structure Preserving Schemes for the Cahn-Hilliard-Navier-Stokes Equations with Degenerate Mobility and Adaptive Mesh Refinement

2026-02-09

AI Summary

This work addresses the challenge of preserving essential physical structures—such as mass conservation, boundedness of the phase-field variable, and energy dissipation—in phase-field simulations of multiphase flows with degenerate mobility. To this end, the authors propose a decoupled implicit–explicit time integration framework that combines a discontinuous Galerkin discretization for the Cahn–Hilliard equation with a continuous Galerkin method for the Navier–Stokes equations, augmented by an interface-adaptive mesh refinement strategy. Through systematic comparisons of various structure-preserving schemes under degenerate mobility and adaptive meshing, the study demonstrates that the proposed approach rigorously maintains key physical properties in canonical test cases, such as the rising bubble, while significantly enhancing computational efficiency and accuracy.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Machine Learning: Structured Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

The Cahn-Hilliard-Navier-Stokes (CHNS) system utilizes a diffusive phase-field for interface tracking of multi-phase fluid flows. Recently structure preserving methods for CHNS have moved into focus to construct numerical schemes that, for example, are mass conservative or obey initial bounds of the phase-field variable. In this work decoupled implicit-explicit formulations based on the Discontinuous Galerkin (DG) methodology are considered and compared to existing schemes from the literature. For the fluid flow a standard continuous Galerkin approach is applied. An adaptive conforming grid is utilized to further draw computational focus on the interface regions, while coarser meshes are utilized around pure phases. All presented methods are compared against each other in terms of bound preservation, mass conservation, and energy dissipation for different examples found in the literature, including a classical rising droplet problem.

Problem

• Cahn-Hilliard-Navier-Stokes
• structure preserving
• degenerate mobility
• adaptive mesh refinement
• phase-field

Innovation

• Structure preserving schemes
• Discontinuous Galerkin method
• Adaptive mesh refinement
• Degenerate mobility
• Cahn-Hilliard-Navier-Stokes equations