GMUSTA scheme to solve a two-phase morphodynamic model for simulations of dam breaching by overtopping

The majority of past dam failures occurred with earthfill dams due to breaching by overtopping under extreme hydrologic events, which involves high-intensity sediment transport and rapid change in bed elevations due to erosion/deposition. Equally important is the failure of earthen levees protecting flood-prone areas. High extreme hydrological events may lead to overtopping, followed by erosion and gradual failure. The dynamics of this process and its modeling are the same as for earthen dams. The rate of breaching strongly influences the height and shape of the ensuing flood wave. The prediction of the breach evolution is, thus, of particular interest to disaster relief planners. Two-phase morphodynamic models are gaining increasing interest to study these problems since they take into account the momentum of the sediment transport, which may be varying almost with the same time scale as flow, and do not require a semi-empirical sediment transport equation developed for steady equilibrium flows. Numerical solution of two-phase models requires accurate tracking of water and sediment perturbations, and presents challenges due to the complex eigenstructure. Classical Godunov methods do not apply due to the difficulty of writing a generalized Riemann problem involving both water and sediment phases. Moreover, even if it exists, the corresponding Riemann problem may be too costly to solve numerically. The present study circumvents this difficulty by employing the multi-stage GMUSTA method proposed by Toro and Titarev (2006) to solve a two-phase morphodynamic model developed by Greco et al. (2008). In this method, the intercell fluxes are computed using GFORCE flux (an average of Lax-Friedrichs and Lax-Wendroff fluxes) via multi-stage predictor-corrector steps. The solution of the Riemann problem is approximated by defining an independent, local space-time MUSTA mesh centered on the interface. Upwinding is achieved through multi-staging by using a conservative scheme to advance the left and right states through time. The main advantage of this scheme is its simplicity while approaching the accuracy of upwind schemes. The paper describes the two-phase model and its numerical solution using a one-stage GMUSTA method. The results of simulation of laboratory test cases show that the proposed numerical method is highly efficient and produces results that are in agreement with experimental data.