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Abstract. We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The fluid flow is modeled by the time-dependent Navier- Stokes equations in a three-dimensional cylindrical domain, while the lateral wall of the cylinder is modeled by the two-dimensional linearly elastic Koiter shell equations coupled to a one-dimensional system of conservation laws defined on a graph domain, describing a mesh of curved rods. The mesh supported shell allows displacements in all three spatial directions. Two-way coupling based on kinematic and dynamic coupling conditions is assumed between the fluid and composite structure, and between the mesh of curved rods and Koiter shell. Problems of this type arise in many ap- plications, including blood flow through arteries treated with vascular prostheses called stents. We prove the existence of a weak solution to this nonlinear, moving boundary problem by using the time discretization via Lie operator splitting method combined with an Arbitrary Lagrangian-Eulerian approach, and a non-trivial extension of the Aubin-Lions-Simon compactness result to problems on moving domains.
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Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems
As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.
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- Award ID(s):
- 1835674
- PAR ID:
- 10349476
- Date Published:
- Journal Name:
- Fluids
- Volume:
- 6
- Issue:
- 12
- ISSN:
- 2311-5521
- Page Range / eLocation ID:
- 460
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.3390/fluids6120460
