ABSTRACT
Solid material advected by a fluid flow may contribute significantly to the momentum balance. Of special interest are highly unsteady free-surface flows like flash floods, dam-break flows or tsunamis propagating inland; these flows possess an enormous potential of incorporating solids, as exemplified by the debris-flow events in Madeira Islands, 2011 , or shown in video footages of the Tohoku tsunami disaster. The motion of the solid mass may be difficult to predict due to the complexity of the modes of momentum transfer by the fluid motion and due to its interactions with other solids. A unified discretization of rigid solids and fluids that allows for detailed and resolved simulations of the fluid-solid phases is presented. The model is based on the fundamental conservation laws of hydrodynamics, namely the continuity and Navier-Stokes equations, and the equation of conservation of momentum of solid bodies. Details of contact mechanics are derived from state-of-the-art formulations considering normal and frictional contacts. The coupled numerical solution, based on the fully meshless lagrangean method Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM), resolves solid-solid and solid-fluid interactions in a broad range of scales. This method allows for a detailed description of momentum transfer at solid boundaries and allows for upscaling the flow description to large scales typical of engineering problems, such as transport of debris or hydrodynamic actions on structures. Such class of simulations, due to the size of the domain and required resolutions, are made practical due to a careful implementation using novel, highly parallel, computational architectures as the GPU. General overviews of the conceptual models, numerical discretization and implementation are addressed, and results for complex multiphasic flows are shown. Initial validations based on experimental work are drawn and discussed.
