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This study proposes a model based on the combination of Smoothed Particle Hydrodynamics, Coarse Grained Molecular Dynamics and the Discrete Element Method for the simulation of dispersed solid-liquid flows. The model can deal with a large variety of particle types (non-spherical, elastic, breakable, melting, solidifying, swelling), flow conditions (confined, free-surface, microscopic), and scales (from microns to meters). Various examples, ranging from biological fluids to lava flows, are simulated and discussed. In all cases, the model captures the most important features of the flow.

The hemodynamics in flexible deep veins valves is modelled by means of discrete multi-physics and an agglomeration algorithm is implemented to account for blood accrual in the flow. Computer simulations of a number of valves typologies are carried out. The results show that the rigidity and the length of the valve leaflets play a crucial role on both mechanical stress and stagnation in the flow. Rigid and short membranes may be inefficient in preventing blood reflux, but reduce the volume of stagnant blood potentially lowering the chances of thrombosis. Additionally, we also show that in venous valves, cell agglomeration is driven by stagnation rather than mechanical stress.

We propose a mesh-free and discrete (particle-based) multi-physics approach for modelling the hydrodynamics in flexible biological valves. In the first part of this study, the method is successfully validated against both traditional modelling techniques and experimental data. In the second part, it is further developed to account for the formation of solid aggregates in the flow and at the membrane surface. Simulations of various types of aggregates highlight the main benefits of discrete multi-physics and indicate the potential of this approach for coupling the hydrodynamics with phenomena such as clotting and calcification in biological valves.

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