Quantifying multiple uncertainties in modelling shallow water-sediment flows: A stochastic Galerkin framework with Haar wavelet expansion and an operator-splitting approach

The interactive processes of shallow water flow, sediment transport, and morphological evolution constitute a hierarchy multi-physical problems significant interests in spectrum engineering science areas. To date, modelling hydro-sediment-morphodynamic (SHSM) is subject to multiple sources uncertainty arising from input data incomplete understanding the underlying physics. A stochastic SHSM model with uncertainties has yet be developed as most models still concern deterministic only one been recently extended setting, but restricted single source uncertainty. Here we first present new probabilistic incorporating within Galerkin framework using multidimensional tensor product Haar wavelet expansion capture local, nonlinear variations joint probability distributions an operator-splitting-based method ensure that system remains hyperbolic. Then, verify proposed via benchmark numerical tests introduced initial boundary conditions, matching established experiments flow-sediment-bed evolutions driven by sudden dam break landslide failure large-scale rapid response flash flood. work facilitates promising for quantifying practical applications.