A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916333629734912 |
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| author | Gao, Yali Han, Daozhi Sarkar, Sayantan |
| author_facet | Gao, Yali Han, Daozhi Sarkar, Sayantan |
| contents | A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the $Q_k$ finite element with mass lumping on rectangular grids, the second-order convex splitting method, and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key to bound-preservation is the discrete $L^1$ estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations Gao, Yali Han, Daozhi Sarkar, Sayantan Numerical Analysis Analysis of PDEs A high-order numerical method is developed for solving the Cahn-Hilliard-Navier-Stokes equations with the Flory-Huggins potential. The scheme is based on the $Q_k$ finite element with mass lumping on rectangular grids, the second-order convex splitting method, and the pressure correction method. The unique solvability, unconditional stability, and bound-preserving properties are rigorously established. The key to bound-preservation is the discrete $L^1$ estimate of the singular potential. Ample numerical experiments are performed to validate the desired properties of the proposed numerical scheme. |
| title | A high-order accurate unconditionally stable bound-preserving numerical scheme for the Cahn-Hilliard-Navier-Stokes equations |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2407.16498 |