A GPU-accelerated Efficient Simulation Tool (EST) for 2D variable-density mud/debris flows over non-uniform erodible beds

Abstract

Mud/debris flows are among the most challenging gravity-driven flows in environmental and geophysical processes. Natural muddy slurries and debris are solid-laden fluids where the density of the mixture can be more than twice or three times the water density and, hence, the bulk solid phase can represent 40–80% of the flow column volume. Furthermore, these unsteady flows usually occur along steep and irregular terrain which requires a refined non-structured spatial discretization, increasing the computational times of the models. In this work a new upwind Roe-type solver for two-dimensional multi-grain mixture shallow-flow over non-uniform erodible bed is presented. The coupled system of depth-averaged equations is formed by the conservation equations for the mass and momentum of the variable-density mixture, the mass conservation equations for the N different solid phases transported in the flow and the continuity equation for the erodible bed layer, where the different solid phases can be exchanged independently modifying the bed level. The non-Newtonian rheological behavior of the multi-grain mixture is included into the momentum equations using six different basal resistance formulations. An accurate, robust and efficient x-split Augmented Roe (xA-Roe) solver for variable-density flow is derived, which requires a complete reformulation of the averaged-Roe values at the intercell edges and allows the mixture density to participate in the definition of the characteristic wave celerities of the local Riemann problem. The global time step is dynamically controlled by the wave celerities of the coupled system of equations, preserving the scheme stability even for high density gradients. The bed slope and basal resistance source terms are also upwind discretized and included into the intercell numerical fluxes, ensuring a well-balanced flux formulation in steady states and the correct treatment of wet-dry fronts. The proposed model is GPU-accelerated using a CUDA/C++ algorithm and applied to synthetic tests and the USGS debris dambreak experiments over erodible bed, demonstrating its robustness, accuracy and efficiency. Finally, the model is tested against a real-scale and long-term case, the mining-tailing dam failure occured in Brumadinho (Brazil) in 2019. The numerical results show good agreement with the observed field data and the computational cost reduction obtained with the GPU-accelerated algorithm is up to 60 times compared to a CPU-based code.