A new class of sediment transport models for dam break problems

During sudden dam breaks in shallow water environments, the water fluctuations with greater lengths of correlations are more intense. As consequence, the water flow becomes rapid and mobilizes sediments, while simultaneously modifying the bottom interface. The existing literature does not provide an averaged sediment transport model (STM) that accounts for both mean and fluctuating motions over an abrupt mobile sediment bottom. Averaged shallow water based models are frequently employed to describe sediment transport in shallow water environments. However, they are not still applicable when the flow becomes turbulent as observed during sudden dam breaks. The aforementioned classical models consider solely the mean motion of water and such consideration provides an inaccurate description of the wavefront profiles. To account the fluctuating motion of water in a STM, we will assume that \(|u -\overline{u}|^k \le \tau ^k h, \;\; k>0\), where h is the water depth such that \(|h| = \mathscr {O}(\varepsilon )\). Additionally, we assume a weakly concentrated approximation to derive the model. The new derived model in this study builds upon previous work by several authors in 1980–2007, 2012, and 2018, while also improving upon more recent models developed in 2022 and 2023. The hyperbolic STM is subject to various complexities arising from turbulence and several nonlinear coupled terms. Furthermore, solving this problem still poses a computational challenge in terms of accuracy, convergence, robustness, and efficiency. To address this challenge, we propose a new first-order path-conservative method based on HLL Riemann solver named \(\text {HLL}_{**}\). The second-order scheme is achieved by using a modified Averaging Essentially Non-Oscillatory (AENO) nonlinear reconstruction. This method is noteworthy because it generalizes several HLL-based schemes developed in recent years. Several dam break tests have been performed to assess the developed modeling. It was observed that all the admissible weak solutions of the model are numerically well represented. Furthermore, it was determined that the model improves the description of the movements of the two successive slow/fast interfaces driven by a shock. The proposed numerical modeling improves also the description of the water depth profile and the propagation of wavefronts during a dam break. The scheme captures all the admissible erosional shocks that improve the description the behavior of the bottom interface.