Abstract
We propose a computational method for the coupled simulation of a compressible flow interacting with a thin-shell structure undergoing large deformations. An Eulerian finite volume formulation is adopted for the fluid and a Lagrangian formulation based on subdivision finite elements is adopted for the shell response. The coupling between the fluid and the solid response is achieved via a novel approach based on level sets. The basic approach furnishes a general algorithm for coupling Lagrangian shell solvers with Cartesian grid based Eulerian fluid solvers. The efficiency and robustness of the proposed approach is demonstrated with an airbag deployment simulation. It bears emphasis that in the proposed approach the solid and the fluid components as well as their coupled interaction are considered in full detail and modeled with an equivalent level of fidelity without any oversimplifying assumptions or bias towards a particular physical aspect of the problem.
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References
Radovitzky, R. and Ortiz, M., “Lagrangian finite element analysis of Newtonian fluid flows,” International Journal For Numerical Methods In Engineering, Vol. 43, No. 4, 1998, pp. 607–617.
Donea, J., “An arbitrary Lagrangian-Eulerian finite element method for transien-t fluid-structure interactions,” Computer Methods in Applied Mechanics and Engineering, Vol. 33, 1982, pp. 689–723.
Fedkiw, R., Aslam, T., Merriman, B., and Osher, S., “A Non-Oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (The Ghost Fluid Method),” J. Comput. Physics, Vol. 152, 1999, pp. 457–492.
Cummings, J., Aivazis, M., Samtaney, R., Radovitzky, R., Mauch, S., and Meiron, D.,“A virtual test facility for the simulation of dynamic response in materials,” Journal of Supercomputing, Vol.23, No. 1, 2002, pp. 39–50.
Meiron, D., Radovitzky, R., and Samtaney, R., “The Virtual Test Facility: An Environment For Simulating The Nonlinear Dynamic Response of Solids Under Shock And Detonation Wave Loading,” Proceedings of the Sixth U.S. National Congress on Computational Mechanics, U.S. Association for Computational Mechanics, Dearborn, MI, 2001.
Mauch, S., “A Fast Algorithm for Computing the Closest Point and Distance Transform,” Preprint, http://www.acm.caltech.edu/~seanm/software/cpt/cpt.html/~seanm/software/cpt/cpt.html, 2001.
Cirak, F. and Ortiz, M., “FullyC 1-Conforming Subdivision Elements for Finite Deformation Thin-Shell Analysis,” Internat. J. Numer. Methods Engrg., Vol.51, 2001, pp. 813–833.
Cirak, F., Ortiz, M., and Schröder, P., “Subdivision Surfaces: A New Paradigm for Thin-Shell Finite-Element Analysis,” Internat. J. Numer. Methods Engrg., Vol. 47, No. 12, 2000, pp. 2039–2072.
Marsden, J. E. and Hughes, T. J. R., Mathematical foundations of elasticity, Prentice-Hall, Englewood Cliffs, N.J., 1983.
Samtaney, R. and Zabusky, N. J., “Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws,” J. Fluid Mech., Vol. 269, 1994, pp. 45–78.
Samtaney, R. and Meiron, D. I., “Hypervelocity Richtmyer-Meshkov instability,” Phys. Fluids, Vol. 9, No. 6, 1997, pp. 1783–1803.
Pullin, D. I., “Direct simulation methods for compressible ideal gas flow.” J. Comput. Phys., Vol. 34, 1980, pp. 231–244.
LevVeque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.“ASCI Alliance Center for the Simulation of Dynamic Response of Materials, FY00 Annual Report,” URL: http:// www.cacr.caltech.edu/ ASAP/onlineresources/publications//ASAP/onlineresources/publications/, 2000.
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Cirak, F., Radovitzky, R. (2003). A New Lagrangian-Eulerian Shell-Fluid Coupling Algorithm Based on Level Sets. In: Benaroya, H., Wei, T.J. (eds) IUTAM Symposium on Integrated Modeling of Fully Coupled Fluid Structure Interactions Using Analysis, Computations and Experiments. Fluid Mechanics and its Applications, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0995-9_34
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DOI: https://doi.org/10.1007/978-94-007-0995-9_34
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3762-4
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