In this paper, two different classes of transient algorithms, implicit-explicit and implicit-implicit, are developed for the response calculations of long-time duration fluid structure interaction problems which arise during a seismic event. To avoid the stringent time step, the generalized structural and fluid displacements are integrated implicitly. If the fluid wave effect is important (e.g., dam-reservoirs and fluid-pipe systems), the second-order accuracy explicit Rational Runge-Kutta (RRK) operator is employed to integrate the fluid pressure. If the fluid is incompressible or the fluid inertia is much greater than that due to the structure (e.g., fluid-tank systems and nuclear reactor systems), the implicit generalized trapezoidal family of methods are employed to integrate the fluid pressure. With the implicit-explicit partition, the advantage of employing larger time step is achieved; whereas with the implicit-implicit partition, unconditional stability is sought. The resulting coupled matrix equations are “symmetric” and “profiled,” and there is only one structural response calculation per time step. The accuracy and stability of these two algorithms are studied via an elastic piston wave interaction problem. The economical advantages in both computations and computer storage are examined on the problem of a fluid-pipe system.
Efficient Computational Procedures for Long-Time Duration Fluid-Structure Interaction Problems
Liu, W. K., and Chang, H. G. (November 1, 1984). "Efficient Computational Procedures for Long-Time Duration Fluid-Structure Interaction Problems." ASME. J. Pressure Vessel Technol. November 1984; 106(4): 317–322. https://doi.org/10.1115/1.3264358
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