Deformable bodies in a 3-dimensional viscous flow: Vorticity-Stream vector formulation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917190725271552 |
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| author | Gallen, Andreu F. Biosca, Joan Muñoz Castro, Mario Hernández-Machado, Aurora |
| author_facet | Gallen, Andreu F. Biosca, Joan Muñoz Castro, Mario Hernández-Machado, Aurora |
| contents | When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a novel numerical formulation for simulating incompressible viscous flows at low Reynolds numbers in the presence of deformable interfaces. Our method employs a vorticity-stream vector formulation that significantly simplifies the fluid solver, transforming it into a set of coupled Poisson problems. The body-fluid interface is modeled using a phase field, allowing for the incorporation of various free-energy models to account for membrane bending and surface tension. In contrast to existing three-dimensional approaches, such as Lattice Boltzmann Methods or boundary-integral techniques, our formulation is lightweight and grounded in classical fluid mechanics principles, making it implementable with standard finite-difference techniques. We demonstrate the capabilities of our method by simulating the evolution of a single vesicle or droplet in Newtonian Poiseuille and Couette flows under different free-energy models, successfully recovering canonical axisymmetric shapes and stress profiles. Although this work primarily focuses on single-body dynamics in Newtonian suspending fluids, the framework can be extended to include body forces, inertial effects, and viscoelastic media. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05031 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformable bodies in a 3-dimensional viscous flow: Vorticity-Stream vector formulation Gallen, Andreu F. Biosca, Joan Muñoz Castro, Mario Hernández-Machado, Aurora Fluid Dynamics Biological Physics When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a novel numerical formulation for simulating incompressible viscous flows at low Reynolds numbers in the presence of deformable interfaces. Our method employs a vorticity-stream vector formulation that significantly simplifies the fluid solver, transforming it into a set of coupled Poisson problems. The body-fluid interface is modeled using a phase field, allowing for the incorporation of various free-energy models to account for membrane bending and surface tension. In contrast to existing three-dimensional approaches, such as Lattice Boltzmann Methods or boundary-integral techniques, our formulation is lightweight and grounded in classical fluid mechanics principles, making it implementable with standard finite-difference techniques. We demonstrate the capabilities of our method by simulating the evolution of a single vesicle or droplet in Newtonian Poiseuille and Couette flows under different free-energy models, successfully recovering canonical axisymmetric shapes and stress profiles. Although this work primarily focuses on single-body dynamics in Newtonian suspending fluids, the framework can be extended to include body forces, inertial effects, and viscoelastic media. |
| title | Deformable bodies in a 3-dimensional viscous flow: Vorticity-Stream vector formulation |
| topic | Fluid Dynamics Biological Physics |
| url | https://arxiv.org/abs/2601.05031 |