Comparison of Structure-Preserving Methods for the Cahn-Hilliard-Navier-Stokes Equations
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| Format: | Preprint |
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2026
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| _version_ | 1866915836715859968 |
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| author | Gunnarsson, Jimmy Kornelije Klöfkorn, Robert |
| author_facet | Gunnarsson, Jimmy Kornelije Klöfkorn, Robert |
| contents | We develop structure-preserving discontinuous Galerkin methods for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility. The proposed SWIPD-L and SIPGD-L methods incorporate parametrized mobility fluxes with edge-wise mobility treatments for enhanced coercivity-stability control. We prove coercivity for the generalized trilinear form and demonstrate optimal convergence rates while preserving mass conservation, energy dissipation, and the discrete maximum principle. Comparisons with existing SIPG-L and SWIP-L methods confirm similar stability. Validation on $hp$-adaptive meshes for both standalone Cahn-Hilliard and coupled systems shows significant computational savings without accuracy loss. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_22861 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comparison of Structure-Preserving Methods for the Cahn-Hilliard-Navier-Stokes Equations Gunnarsson, Jimmy Kornelije Klöfkorn, Robert Numerical Analysis Mathematical Physics We develop structure-preserving discontinuous Galerkin methods for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility. The proposed SWIPD-L and SIPGD-L methods incorporate parametrized mobility fluxes with edge-wise mobility treatments for enhanced coercivity-stability control. We prove coercivity for the generalized trilinear form and demonstrate optimal convergence rates while preserving mass conservation, energy dissipation, and the discrete maximum principle. Comparisons with existing SIPG-L and SWIP-L methods confirm similar stability. Validation on $hp$-adaptive meshes for both standalone Cahn-Hilliard and coupled systems shows significant computational savings without accuracy loss. |
| title | Comparison of Structure-Preserving Methods for the Cahn-Hilliard-Navier-Stokes Equations |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2602.22861 |