On numerical approximations to fluid-structure interactions involving compressible fluids

TL;DR

This paper presents a stable and consistent numerical scheme for simulating fluid-structure interactions involving compressible fluids and elastic plates in multiple dimensions.

Contribution

It introduces a fully discrete, stable numerical scheme that ensures geometric conservation, mass conservation, and density positivity for compressible fluid-structure interactions.

Findings

Scheme is stable and mass-conserving

Ensures positivity of density

Proven to be consistent with weak solutions

Abstract

In this paper we introduce a numerical scheme for fluid-structure interaction problems in two or three space dimensions: A flexible elastic plate is interacting with a viscous, compressible barotropic fluid. Hence the physical domain of definition (the domain of Eulerian coordinates) is changing in time. We introduce a fully discrete scheme that is stable, satisfies geometric conservation, mass conservation and the positivity of the density. We also prove that the scheme is consistent with the definition of continuous weak solutions.