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Parameterization-driven arbitrary Lagrangian–Eulerian method for large-deformation isogeometric fluid–structure interaction
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DOI：10.1016/j.cma.2026.119358.png)
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Abstract
En 中文
Body-fitted arbitrary Lagrangian–Eulerian (ALE) methods provide a sharp representation of the fluid–structure interface but rely on mesh-update strategies that incrementally deform a reference configuration. Because each update is applied on top of the previous one, distortion accumulates over time, and large structural motion eventually leads to loss of mesh validity. This path dependence is inherent to the mesh-motion formulation itself: it follows from updating each mesh from the previous one, and cannot be eliminated by refining the underlying extension operator. To address this issue, we reformulate the ALE mesh-motion problem in the isogeometric setting as a sequence of independent domain parameterization problems. At each time step, a multi-patch spline parameterization of the fluid domain is constructed from the current interface geometry; its validity and quality therefore depend on the current configuration alone, not on the cumulative history of mesh deformation. Mesh motion follows directly from this per-step parameterization, rather than being the primary unknown of an auxiliary mesh-extension problem driven by interface displacement, so the cumulative distortion characteristic of classical ALE is absent by construction. Three technical components realize this framework: (i) a barrier-function-based spline parameterization that enforces a strictly positive Jacobian at every time step; (ii) a tangential-slip reparameterization that handles sustained large rotations of closed interfaces, where no fixed boundary-to-parameter correspondence is admissible; and (iii) a constant-preserving quasi-interpolation operator for solution transfer between consecutive parameterizations, which preserves uniform states in the adopted advective ALE update. The framework is formulated in a partitioned setting, so that the fluid and structural solvers remain independent. Our numerical examples start with a purely kinematic example motivating the use of higher-order spline-based mesh formulations over conventional piecewise-linear methods in terms of the maximum allowed deformation the mesh can handle. Thereafter, we validate our method in combination with higher-order isogeometric mesh descriptions on two two-dimensional FSI benchmarks and a prescribed-rotation flow benchmark, covering standard and large-rotation regimes, and on three-dimensional falling-sphere and rotor problems. On the rotating-square benchmark, the tangential-slip strategy sustains continuous rotation beyond the admissible range of conventional mesh-deformation ALE methods with a fixed boundary correspondence. On the Turek–Hron and perpendicular-flap benchmarks, the method reproduces published reference displacements and responses, while the minimum scaled Jacobian remains bounded away from zero throughout the simulation. A prescribed-translation sphere test isolates mesh robustness under a 40 m displacement, and a fully coupled free-fall test reproduces the wall-corrected terminal velocity to within 0.29%. A three-dimensional rotor example further demonstrates that the framework extends naturally to volumetric spline parameterizations. Finally, we show that the per-step spline parameterizations can be used directly within a standard finite element solver, yielding results consistent with the isogeometric solution on the same sequence of geometries. This decoupling of geometry construction from field discretization positions the proposed framework as a solver-agnostic geometry component, compatible with both isogeometric and classical finite-element FSI pipelines. The focus is therefore on the geometry-construction module, rather than on claiming general accuracy or efficiency advantages of isogeometric analysis over finite-element remeshing strategies.
Keywords:
Isogeometric analysis
Fluid–structure interaction
Arbitrary Lagrangian–Eulerian (ALE)
Multi-patch spline parameterization
Large-deformation mesh motion
Journal
IF:
7.3
Papers:
1.3W
Citations:
5.6W