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arXiv · 2101.12088

Projection based model reduction for the immersed boundary method

Yushuang Luo·Xiantao Li·Wenrui Hao
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Abstract

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.

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Yushuang Luo, Xiantao Li, Wenrui Hao. 2021-01-28. Projection based model reduction for the immersed boundary method. https://arxiv.org/abs/2101.12088

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