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

Prof. Robert Klöfkorn, Lund University
Contact: Prof. Dr. Axel Voigt

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 in terms of bound preservation, mass conservation, and energy dissipation for different examples.

[1] Gunnarsson and Klöfkorn. Comparison of structure preserving schemes for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility and adaptive mesh refinement. JCOMP, 2026
DOI https://doi.org/10.1016/j.jcp.2026.115275

[2] Gunnarsson and Klöfkorn. A Discontinuous Galerkin Scheme for the Cahn-Hilliard Equations with Discrete Maximum Principle for Arbitrary Polynomial Order. Submitted to SISC.
DOI: https://doi.org/10.48550/arXiv.2604.0098