Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs

Abstract

A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed using random sampling techniques and non-intrusive methods based on generalized Polynomial Chaos (PC). These methods allow to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution in different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained by the variability in the model input. We finally present a synthetic experiment studying the variance based sensitivity of the wave load on an offshore structure to a number of input uncertainties. In the numerical examples presented the PC methods have exhibited fast convergence, suggesting that the problem is amenable to being analyzed with such methods.

On the relationship between the stochastic Galerkin method and the pseudo-spectral collocation method for linear differential algebraic equations

“…It is worth noting that Theorem 4 is equivalent to Theorem 2 in [14], which relies on the fact that under this assumption the Gauss quadrature utilized by the PSCM reproduces exactly the projection integrals in (12).…”

“…More in general, equation (28) quantifies the error that exists for K > 1 between the matrices defining the SGM and the PSCM problems or, alternatively, the error arising with the PSCM in the computation of the projections in (12). It should be noted that, since the PCE coefficients C k exponentially decay to zero as the order K is increased [2], the above error is expected to converge to a constant value.…”

“…The technique has the relevant advantage of requiring only a set of repeated simulations of the original system at the quadrature nodes, and hence, it is straightforward to implement. It has been recently applied, for example, to the analysis of water wave propagation [12]. Galerkin-and collocation-based approaches have been compared from a numerical viewpoint in [13].…”

Probabilistic modeling and global sensitivity analysis for CO2 storage in geological formations: a spectral approach

“…In particular, we utilize PC expansions to build such surrogates. PC expansions, whose theory goes back to the late 30's and 40's [17,18], have become an increasingly popular tool in recent years as they provide efficient means for performing UQ in computationally intensive mathematical models; see e.g., [19,20,21,22,23,24,10,25,26,27,28,29,30] for a nonexhaustive sample of research contributions to numerical methods for UQ using PC expansions and applications of these methods to real world problems.…”

Lattice Boltzmann Method of a Flooding Accident at Gopeng, Perak, Malaysia

“…The Computational Fluid Dynamics (CFD) model applied in the water sector is a prevailing device to simulate the condition of the fluid especially in urban hydrology and water management field [5]. The ability to investigate the real situation by using a device can help to predict the future condition [6]. Hence, we benefit by comparing and improvising both theory and the real-life situations.…”