Stochastic modelling of fluid-structure interactions

Full text: We propose a new numerical formulation based on polynomial chaos to model uncertainty in large-scale simulations involving incompressible flow-structure interactions. The uncertainty in the coupled system may arise from upstream inflow conditions, free-surface motion, material and constitutive laws of the structure or geometric irregularities such as roughness. This approach provides a more efficient way to simulate the propagation of uncertainties in the system than classical methods such as Monte-Carlo simulation. Randomness becomes a new dimension in addition to the space-time domain. The stochastic Gaussian or non-Gaussian input is spectrally represented using a Karhunen-Loeve or a polynomial chaos decomposition. Wiener-Hermite polynomials from the Askey-scheme of hypergeometric family of polynomials are used as a set of orthogonal polynomial expansions to the stochastic processes. A standard Galerkin projection is performed and the resulting set of coupled equations is solved to obtain the solution for each random modes. The polynomial chaos provides the stochastic solution and therefore all statistics solution in a single run. The first and second terms in the expansion represents the mean solution and the Gaussian part of the solution respectively. Higher modes give information on the non-Gaussianity of the solution. In this work, we simulate a 2D laminar flow past a free circular cylinder with uncertain mechanical properties of the structure or uncertain free-stream inflow. First, we use polynomial chaos to determine the response of linear and nonlinear second order oscillators subject to random excitations. We treat two cases corresponding to mechanical properties being random variables as well as random processes. We present convergence rates of the solution for the different cases. Once we validate our model for the structure, we then couple it to the stochastic Navier-Stokes solver and perform stochastic simulations of vortex induced vibrations. Refs. 3 (author)