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.

我们提出了一种自适应降阶模型，用于对具有复杂和非线性变形的流固耦合问题进行有效的时间分辨模拟。该模型基于结构平衡方程的重复线性化。在每个线性化步骤中，通过使用模态约简大大减少了未知数的数量，从而显着提高了计算效率。每当超过无量纲变形阈值时，通过自适应重新校准和截断增强，我们确保减少的模态基础对小变形和大变形保持任意精度。我们的新模型嵌入到一个分区的、松散耦合的有限体积-有限元框架中，其中欧拉流体求解器内的结构界面运动由保守的切割单元浸入边界方法解释。在超音速下平板的气动弹性不稳定性、放置在激波管内的弹性面板以及膨胀的薄半球的冲击引起的屈曲的应用证明了该方法的效率和准确性。