Anisotropic mesh adaptation for unsteady two-phase flow simulation with the Cahn-Hilliard Navier-Stokes model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909869571833856 |
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| author | Bawin, Arthur Étienne, Stéphane Béguin, Cédric |
| author_facet | Bawin, Arthur Étienne, Stéphane Béguin, Cédric |
| contents | We present an anisotropic mesh adaptation procedure based on Riemannian metrics for the simulation of two-phase incompressible flows with non-matching densities. The system dynamics are governed by the Cahn-Hilliard Navier-Stokes (CHNS) equations, discretized with mixed finite elements and implicit time-stepping. Spatial accuracy is controlled throughout the simulation by the \emph{global transient fixed-point method} from Alauzet \emph{et al.}, in which the simulation time is divided into sub-intervals, each associated with an adapted anisotropic mesh. The simulation is run in a fixed-point loop until convergence of each mesh--solution pair. Each iteration takes advantage of the previously computed solution and accurately predicts the flow variations. This ensures that the mesh always captures the fluid-fluid interface, and allows for a dynamic control of the interface thickness at a fraction of the computational cost compared to uniform or isotropic grids. Moreover, using a modest number of time sub-intervals reduces the transfer error from one mesh to another, which would otherwise eventually spoil the numerical solution. The overall adaptive procedure is verified with manufactured solutions and the well-known rising bubble benchmark. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anisotropic mesh adaptation for unsteady two-phase flow simulation with the Cahn-Hilliard Navier-Stokes model Bawin, Arthur Étienne, Stéphane Béguin, Cédric Numerical Analysis Computational Physics Fluid Dynamics We present an anisotropic mesh adaptation procedure based on Riemannian metrics for the simulation of two-phase incompressible flows with non-matching densities. The system dynamics are governed by the Cahn-Hilliard Navier-Stokes (CHNS) equations, discretized with mixed finite elements and implicit time-stepping. Spatial accuracy is controlled throughout the simulation by the \emph{global transient fixed-point method} from Alauzet \emph{et al.}, in which the simulation time is divided into sub-intervals, each associated with an adapted anisotropic mesh. The simulation is run in a fixed-point loop until convergence of each mesh--solution pair. Each iteration takes advantage of the previously computed solution and accurately predicts the flow variations. This ensures that the mesh always captures the fluid-fluid interface, and allows for a dynamic control of the interface thickness at a fraction of the computational cost compared to uniform or isotropic grids. Moreover, using a modest number of time sub-intervals reduces the transfer error from one mesh to another, which would otherwise eventually spoil the numerical solution. The overall adaptive procedure is verified with manufactured solutions and the well-known rising bubble benchmark. |
| title | Anisotropic mesh adaptation for unsteady two-phase flow simulation with the Cahn-Hilliard Navier-Stokes model |
| topic | Numerical Analysis Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2510.21749 |