Multi-level Monte Carlo finite volume method for shallow water equations with uncertain parameters applied to landslides-generated tsunamis

Two layer Savage-Hutter type shallow water PDEs model flows such as tsunamis generated by rockslides. On account of heterogeneities in the composition of the granular matter, these models contain uncertain parameters like the ratio of densities of layers, Coulomb and interlayer friction. These parameters are modeled statistically and quantifying the resulting solution uncertainty (UQ) is a crucial task in geophysics. We propose a novel paradigm for UQ that combines the recently developed IFCP spatial discretizations with the recently developed Multi-level Monte Carlo (MLMC) statistical sampling method and provides a fast, accurate and computationally efficient framework to compute statistical quantities of interest. Numerical experiments, including realistic simulations of the Lituya Bay mega tsunami, are presented to illustrate the robustness of the proposed UQ algorithm.