Open-source immersogeometric analysis of fluid–structure interaction using FEniCS and tIGAr

We recently developed the open-source library tIGAr, which extends the FEniCS finite element automation framework to isogeometric analysis. The present contribution demonstrates the utility of tIGAr in complex problems by applying it to immersogeometric fluid–structure interaction (FSI) analysis. This application is implemented as the new open-source library CouDALFISh (Coupling, via Dynamic Augmented Lagrangian, of Fluids with Immersed Shells, pronounced “cuttlefish”), which uses the dynamic augmented Lagrangian (DAL) method to couple fluid and shell structure subproblems. The DAL method was introduced previously, over a series of papers largely focused on heart valve FSI, but an open-source implementation making extensive use of automation to compile numerical routines from high-level mathematical descriptions brings newfound transparency and reproducibility to these earlier developments on immersogeometric FSI analysis. The portions of CouDALFISh that do not use code generation also illustrate how a framework like FEniCS remains useful even when some functionality is outside the scope of its standard workflow. This paper summarizes the workings of CouDALFISh and documents a variety of benchmarks demonstrating its accuracy. Although the implementation emphasizes transparency and extensibility over performance, it is nonetheless demonstrated to be sufficient to simulate 3D FSI of an idealized aortic heart valve. Source code will be maintained at https://github.com/david-kamensky/CouDALFISh.