Numerical investigation of the membrane fluid-structure-interaction problem

Abstract

A fluid-structure-interaction problem comprising a membrane interacting with an aerodynamic flow is of interest for research focused on the behavior of flexible aerospace structures. However, there are no systematic studies available in literature considering this type of problem. The present work examines the numerical solution method and the typical solutions for a 1D vibrating membrane, i.e. a vibrating string, subject to an Euler flow. To assess the vibrating string behavior we present a non-dimensionalization of the fluid-structure-interaction equations, showing us 3 similarity parameters characterizing the interaction system. Furthermore we present a specific space-time finite-element discretization technique for the structure part based on the discontinuous Galerkin method. To relate the discontinuous elements we introduce Riemann solutions on the inter-element boundaries. Accordingly we rewrite the vibrating string equation into a system of first order wave equations. In the numerical results section we show that the non-conventional discretization of the structure equations leads to a stable and consistent numerical scheme by verifying the convergence behavior. Moreover, we present the typical solutions of the vibrating string driven by an Euler flow.