Towards stable coupling methods for high-order discretization of fluid-structure interaction: Algorithms and observations

Authors:
Robert M. Kirby;Zohar Yosibash;George Em Karniadakis
Affiliations:
School of Computing, University of Utah, 50 South Central Campus Dr., Room 3190, Salt Lake City, UT 84112, USA;Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel;Division of Applied Mathematics, Brown University, Providence, RI, USA
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

Weak coupling of an explicit spectral/hp finite element ALE fluid solver with a Chebyshev collocation structural solver for fluid-structure interaction problems is addressed. When attempting to couple high-order spatial discretizations of both fluid and structural phenomena, we are required to consider first principles in order to answer two important questions: (1) What information (e.g. forces, velocities, displacements) does one transfer and when? and (2) How does one transfer information? Our goal is to address these questions by considering a non-conventional transfer of velocities of the wet-surface from the structure to the fluid, and the usual transfer of pressures on the wet-surface from the fluid to the structure. A subsonic three-dimensional compressible flow over an elastic non-linear plate model is considered as a representative example problem and we explore the various function spaces in which data (such as pressures, velocities and displacements) lie. We provide arguments as to what projection algorithms to use in combination with a time-staggering scheme to achieve stable and accurate results and at the same time to retain a temporal second-order scheme. We demonstrate the proposed algorithms by numerical examples considering long time integration.