Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania, USA.
Int J Numer Method Biomed Eng. 2022 Feb;38(2):e3558. doi: 10.1002/cnm.3558. Epub 2021 Dec 9.
Fluid-structure interactions are central to many biomolecular 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 the 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 (ROM) is shown to preserve the Lyapunov stability. We also address the practical issue of computing coefficient matrices in the ROM using an interpolation technique. The efficiency and robustness of the proposed formulation are examined with test examples from various applications.
流固耦合在许多生物分子过程中至关重要，这给计算和建模方法带来了巨大的挑战。在本文中，我们考虑了生物流体系统的浸入边界方法 (IBM)，并应用降阶技术来减轻计算成本，从而消除与大量流体变量相关的自由度。我们展示了如何使用 Petrov-Galerkin 投影和保持不可压缩条件的子空间来导出降阶模型。更重要的是，降阶模型 (ROM) 被证明可以保持 Lyapunov 稳定性。我们还使用插值技术解决了在 ROM 中计算系数矩阵的实际问题。通过来自各种应用的测试示例，检验了所提出的公式的效率和鲁棒性。
