  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.
