Projection‐based model reduction for the immersed boundary method

Abstract

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.

Stability Preserving Data-driven Models With Latent Dynamics

“…In the context of fluid-structure interactions, observed data include time series of the structure, e.g., interfaces. Latent variables act as a reduction of the high-dimensional fluid variables [32]. A prescribed force exerted by the structure is coupled to the latent variables.…”