A monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction model

TL;DR

This paper introduces a new monolithic divergence-conforming HDG scheme for linear fluid-structure interaction problems, achieving energy stability, divergence-free velocity, and efficient solvability with advanced preconditioning.

Contribution

The paper develops a novel divergence-conforming HDG scheme that is pressure-robust, energy stable, and exactly divergence-free for FSI problems with a thick structure.

Findings

Achieves pressure-robust optimal energy-norm estimates.

Produces an exactly divergence-free fluid velocity approximation.

Uses a symmetric indefinite linear system solved efficiently with block AMG preconditioning.

Abstract

We present a novel monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction (FSI) problem with a thick structure. A pressure-robust optimal energy-norm estimate is obtained for the semidiscrete scheme. When combined with a Crank-Nicolson time discretization, our fully discrete scheme is energy stable and produces an exactly divergence-free fluid velocity approximation. The resulting linear system, which is symmetric and indefinite, is solved using a preconditioned MinRes method with a robust block algebraic multigrid (AMG) preconditioner.