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Neishlos, H.; Israeli, M.; Kivity, Y.

The stability of explicit difference schemes for solving the problem of interaction between a compressible fluid and an elastic shell. (English) Zbl 0521.73072

Comput. Methods Appl. Mech. Eng. 41, 129-143 (1983).
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MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S99 Numerical and other methods in solid mechanics

Keywords:

interaction between compressible fluid and elastic shell; initial boundary value problem; partial differential equations; discretized in time and space; explicit difference schemes; Kreiss theory; stability properties influenced by type of discretization in space; contact condition on interface between fluid and shell; approximation of hydrodynamic pressure on surface of shell; sufficient condition; best possible stability properties
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References:

[1] Neishlos, H.; Israeli, M.; Kivity, Y., Stability of some explicit difference schemes for fluid-structure interaction problems, Comput. & Structures, 13, 97-101 (1980) · Zbl 0456.73065
[2] Belytschko, T., Fluid-structure interaction, Comput. & Structures, 12, 459-469 (1980) · Zbl 0457.73076
[3] Hughes, T. Y.R.; Liu, W. K., Implicit-explicit finite elements, in transient analysis: stability theory, ASME J. Appl. Mech., 45, 371-374 (1978) · Zbl 0392.73076
[4] Felippa, C. A.; Park, K. C., Staggered transient analysis procedures for coupled mechanical systems: formulation, Comput. Meths. Appl. Mech. Engrg., 24, 61-111 (1980) · Zbl 0453.73091
[5] Jones, A. V., Fluid-structure coupling with ICE hydrodynamics, Transactions of the 6th International Conference on Structural Mechanics in Reactor Technology, Vol. B, B1/1 (1981), Paris
[6] Gustafsson, B.; Kreiss, H. O.; Sundström, A., Stability theory of difference approximations for mixed initial boundary value problems II, Math. Comput., 26, 679-686 (1972) · Zbl 0293.65076
[7] Michelson, D., Initial-boundary value problems for hyperbolic equations and their difference approximation with uniformly characteristic boundary, (Ph.D. thesis (1980), Tel-Aviv University)
[8] Dahlquist, G.; Björck, A., Numerical Methods, ((1974), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ), 311-318
[9] Parlett, B. N., The Symmetric Eigenvalue Problem, ((1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ), 126-187 · Zbl 0431.65017
[10] Israeli, M.; Kivity, Y.; Neishlos, H., Stability and accuracy in fluid-structure problems, (Tech. Rept. No. 158 (1979), Computer Science Department, Technion, Israel Institute of Technology) · Zbl 0456.73065
[11] Kivity, Y.; Tzur, D., Study of projectile formation in lined shallow cavity charges, (Proc. 4th Inst. Symp. Ballistics. Proc. 4th Inst. Symp. Ballistics, Monterey, CA (1972))
[12] Neishlos, H.; Israeli, M.; Kivity, Y., A coupling algorithm for fluid and structure with different time steps, (Hinton, E.; etal., Numerical Methods for Coupled Problems (1981), Pineridge: Pineridge Swansea), 313-320 · Zbl 0456.73065
[13] Belytschko, T.; Yen, M. J.; Mullen, R., Mixed methods for time integrations, Comput. Meths. Appl. Mech. Engrg., 17/18, 259-275 (1979) · Zbl 0403.73002
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