Projection based model reduction for the immersed boundary method

TL;DR

This paper develops a reduced-order modeling approach for the immersed boundary method in biofluid systems, significantly decreasing computational costs while preserving stability and incompressibility, validated through diverse application tests.

Contribution

It introduces a Petrov-Galerkin projection-based reduction technique that maintains stability and incompressibility in immersed boundary simulations.

Findings

Reduced models effectively lower computational costs.

The approach preserves Lyapunov stability.

Validated robustness across various biofluid applications.

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.