We present a generalized polynomial chaos algorithm to model the input uncertainty and its propagation in flow-structure interactions. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as the trial basis in the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach is a generalization of the original polynomial chaos expansion, which was first introduced by N. Wiener (1938) and employs the Hermite polynomials (a subset of the Askey scheme) as the basis in random space. The algorithm is first applied to second-order oscillators to demonstrate convergence, and subsequently is coupled to incompressible Navier-Stokes equations. Error bars are obtained, similar to laboratory experiments, for the pressure distribution on the surface of a cylinder subject to vortex-induced vibrations.
Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division September 13, 2001; revised manuscript received October 29, 2001. Associate Editor: J. Katz.
Xiu , D., Lucor , D., Su , C., and Karniadakis, G. E. (October 29, 2001). "Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos ." ASME. J. Fluids Eng. March 2002; 124(1): 51–59. https://doi.org/10.1115/1.1436089
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