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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2603.26422 |
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| _version_ | 1866911548249735168 |
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| author | Aznaran, Francis R. A. Bukač, Martina Muha, Boris |
| author_facet | Aznaran, Francis R. A. Bukač, Martina Muha, Boris |
| contents | We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier--Stokes equations for a viscous, incompressible fluid, coupled with the incompressible hyperelasticity system, both written in the Eulerian coordinates. This allows the problem to be written in a unified formulation, using a single field for the fluid and structure velocities. To track the position of the domain, we use a phase-field approach, resulting in a coupled Cahn--Hilliard--Navier--Stokes-type of problem for the diffuse interface fluid-structure interaction. Under certain assumptions, we prove the convergence of the diffuse interface model to the sharp interface fluid-structure interaction problem. To solve the problem numerically, we propose a novel, strongly coupled, second-order partitioned computational method where the system is decoupled into the Cahn--Hilliard problem, the transport problem for the left Cauchy--Green deformation tensor, and the Navier--Stokes problem. The problems are solved iteratively until convergence at each time step. The performance of the method is illustrated on two computational examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26422 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The diffuse interface approximation to fluid-structure interaction Aznaran, Francis R. A. Bukač, Martina Muha, Boris Numerical Analysis We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier--Stokes equations for a viscous, incompressible fluid, coupled with the incompressible hyperelasticity system, both written in the Eulerian coordinates. This allows the problem to be written in a unified formulation, using a single field for the fluid and structure velocities. To track the position of the domain, we use a phase-field approach, resulting in a coupled Cahn--Hilliard--Navier--Stokes-type of problem for the diffuse interface fluid-structure interaction. Under certain assumptions, we prove the convergence of the diffuse interface model to the sharp interface fluid-structure interaction problem. To solve the problem numerically, we propose a novel, strongly coupled, second-order partitioned computational method where the system is decoupled into the Cahn--Hilliard problem, the transport problem for the left Cauchy--Green deformation tensor, and the Navier--Stokes problem. The problems are solved iteratively until convergence at each time step. The performance of the method is illustrated on two computational examples. |
| title | The diffuse interface approximation to fluid-structure interaction |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.26422 |