Isogeometric fluid-structure interaction using a mixed continuous/discontinuous Galerkin scheme

TL;DR

The paper presents a CAD-consistent isogeometric FSI framework that pairs a continuous Galerkin solid solver with a discontinuous Galerkin fluid solver, linked through exact interface transfers enabled by Bézier extraction. The approach preserves high regularity of the structural displacement when transferring to the fluid and supports local fluid grid refinement without geometry distortion. It demonstrates competitive accuracy on a membrane wing and the Turek benchmark, with partitioned coupling and explicit time integration suitable for small time steps. This method offers a practical, modular pathway for high-fidelity FSI simulations in engineering applications, and the accompanying Igloo implementation provides a ready-to-use resource for researchers and developers.

Abstract

A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged to enable an exact transfer of the structural displacement to the fluid domain, while using different discretizations and refinements on the two sides of the coupling interface. The proposed approach is applied to the simulation of a compressible flow around an elastic wing membrane and to a classical fluid-structure benchmark involving the flow around a cylinder equipped with a hyper-elastic bar. For both cases, the results obtained are compared to those found in the literature to assess the accuracy of the proposed method.

Figures (27)

• Figure 1: Seven quadratic B-Spline basis functions
• Figure 2: Example of quadratic NURBS curve with four control points
• Figure 3: Example of curve with a new inserted knot
• Figure 4: Example of curve after Bézier extraction procedure
• Figure 5: Example of quadratic NURBS surface with $4 \times 4$ control points