# Adaptive Reduced-Order Modeling for Non-Linear Fluid-Structure Interaction

## TL;DR

This paper introduces an adaptive reduced-order modeling approach for efficient, accurate simulation of complex non-linear fluid-structure interactions, utilizing repeated linearizations and modal reduction within a partitioned computational framework.

## Contribution

The novel method combines adaptive re-calibration with modal reduction and a partitioned fluid-structure coupling to improve efficiency and accuracy in non-linear FSI simulations.

## Key findings

- Efficient simulation of aeroelastic instability at supersonic speeds.
- Accurate modeling of shock-induced buckling phenomena.
- Significant computational savings demonstrated in multiple applications.

## Abstract

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance equations. Upon each linearization step, the number of unknowns is strongly decreased by using modal reduction, which leads to a substantial gain in computational efficiency. Through adaptive re-calibration and truncation augmentation whenever a non-dimensional deformation threshold is exceeded, we ensure that the reduced modal basis maintains arbitrary accuracy for small and large deformations. Our novel model is embedded into a partitioned, loosely coupled finite volume - finite element framework, in which the structural interface motion within the Eulerian fluid solver is accounted for by a conservative cut-element immersed-boundary method. Applications to the aeroelastic instability of a flat plate at supersonic speeds, to an elastic panel placed within a shock tube, and to the shock induced buckling of an inflated thin semi-sphere demonstrate the efficiency and accuracy of the method.