Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to alleviate the computational cost, we apply reduced-order techniques to eliminate the degrees of freedom associated with a large number of fluid variables. We show how reduced models can be derived using Petrov-Galerkin projection and subspaces that maintain the incompressibility condition. More importantly, the reduced-order model is shown to preserve the Lyapunov stability. We also address the practical issue of computing coefficient matrices in the reduced-order model using an interpolation technique. The efficiency and robustness of the proposed formulation are examined with test examples from various applications.
@article{arxiv.2101.12088,
title = {Projection based model reduction for the immersed boundary method},
author = {Yushuang Luo and Xiantao Li and Wenrui Hao},
journal= {arXiv preprint arXiv:2101.12088},
year = {2021}
}