Reduced formulation of a steady fluid-structure interaction problem with parametric coupling

TL;DR

This paper introduces a combined model reduction approach for steady fluid-structure interaction problems, utilizing reduced basis methods for fluid dynamics and free-form deformations for interface geometry, demonstrated on a channel with flexible walls.

Contribution

It presents a novel two-fold reduction technique integrating reduced basis methods and geometric parameterization for steady FSI problems.

Findings

Effective reduction of computational complexity demonstrated

Accurate approximation of fluid-structure interaction with fewer degrees of freedom

Applicable to steady flow in flexible-walled channels

Abstract

We propose a two-fold approach to model reduction of fluid-structure interaction. The state equations for the fluid are solved with reduced basis methods. These are model reduction methods for parametric partial differential equations using well-chosen snapshot solutions in order to build a set of global basis functions. The other reduction is in terms of the geometric complexity of the moving fluid-structure interface. We use free-form deformations to parameterize the perturbation of the flow channel at rest configuration. As a computational example we consider a steady fluid-structure interaction problem: an incmpressible Stokes flow in a channel that has a flexible wall.