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A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction

Published online by Cambridge University Press:  20 August 2015

J. W. Banks  and
B. Sjögreen
J. W. Banks*
Affiliation:
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
B. Sjögreen*
Affiliation:
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
*
Corresponding author.Email:banks20@llnl.gov
Email:sjogreen2@llnl.gov
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Abstract

In multi physics computations where a compressible fluid is coupled with a linearly elastic solid, it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid. In a numerical scheme, there are many ways that velocity- and stress-continuity can be enforced in the discrete approximation. This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes. The analysis shows that depending on the ratio of densities between the solid and the fluid, some numerical interface conditions are stable up to the maximal CFL-limit, while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit. The paper also presents a new interface condition, obtained as a simplified characteristic boundary condition, that is proved to not suffer from any reduction of the stable CFL-limit. Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.

Keywords

65M1235L6035L65Finite difference methodnormal mode analysisfluid/structure interactioncompressible fluidinterface condition.
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 279 - 304
Copyright
Copyright © Global Science Press Limited 2011

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References

[1] Noh, W. F., CEL:a time-dependent, two space dimensional, coupled Eulerian-Lagrange code, in: Alder, B., Fernbach, S., Rotenberg, M. (Eds.), Methods in Computational Physics, Vol. 3, Academic Press, New York, 1964.Google Scholar
[2] Fedkiw, R. P., Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175 (2002), 200–224.CrossRefGoogle Scholar
[3] Löhner, R., Cebral, J., Yang, C., Baum, J. D., Mestreau, E., Charman, C., and Pelessone, D., Large-scale fluid-structure interaction simulations, Comput. Sci. Eng., 6 (2004), 27–37.CrossRefGoogle Scholar
[4] Deiterding, R., Radovitzky, R., Mauch, S. P., Noels, L., Cummings, J. C., and Meiron, D. I., A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading, Eng. Comput., 22 (2006), 325–344.CrossRefGoogle Scholar
[5] LeVeque, R. J., Numerical Methods for Conservation Laws, Birkhauser, Basel, 1992.CrossRefGoogle Scholar
[6] Gustafsson, B., Kreiss, H.-O., and Sundström, A., Stability theory of difference approximations for mixed initial boundary value problems, II, Math. Comput., 26(119) (1972), 649–686.CrossRefGoogle Scholar
[7] Whitham, G. B., Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974.Google Scholar