Parameterization-driven arbitrary Lagrangian-Eulerian method for large-deformation isogeometric fluid-structure interaction

TL;DR

This paper introduces a novel isogeometric ALE method that constructs independent domain parameterizations at each step, enabling large rotations and deformations in fluid-structure interaction simulations.

Contribution

It reformulates ALE mesh motion as independent spline parameterizations, incorporating barrier functions, tangential-slip reparameterization, and solution transfer operators for improved large-deformation FSI modeling.

Findings

Enables stable simulations under large rotations beyond classical methods.

Successfully validated on 2D and 3D FSI benchmarks, including rotor problems.

Extends naturally to volumetric spline parameterizations and standard finite element solvers.

Abstract

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. 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. 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 unbounded cumulative rotations of closed domains, where no fixed boundary-to-parameter correspondence is admissible; and (iii) a constant-preserving quasi-interpolation operator for solution transfer between consecutive parameterizations, ensuring that the discrete geometric conservation law holds algebraically. We validate the method on three two-dimensional FSI benchmarks, covering standard and large-rotation regimes, and on a three-dimensional rotor problem. On a rotating-square benchmark, the tangential-slip strategy enables simulations under sustained rotation far beyond the range accessible to classical mesh-update schemes--a regime that is fundamentally inaccessible to any mesh-deformation formulation, not merely numerically difficult. 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.