Anisotropic mesh adaptation for unsteady two-phase flow simulation with the Cahn-Hilliard Navier-Stokes model

Fuente: arXiv
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Auteurs principaux: Bawin, Arthur, Étienne, Stéphane, Béguin, Cédric
Format: Preprint
Publié: 2025
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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