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Transient dynamics of fracturing media has received significant attention in recent years, and a number of simulation approaches have been developed. One of these is the combined finite-discrete element method (FDEM). FDEM produces complex fracture and fragmentation patterns in processes such as blast loads, blasting, impact, mining, and oil exploration. To address a wide range of multi-physics problems, numerous approaches have been undertaken to introduce fluid into the FDEM transient dynamics, ranging from application-specific gas models to more advanced hydraulic fracture processes and biomedical applications. None of these have been satisfactory in terms of robustness, accuracy or computational efficiency. In this work, a completely new explicit fluid solver has been tailor-made and fully integrated (as opposed to coupled) into the combined finite-discrete element method. The solver addresses transient pressure wave propagation in fluid, fluid viscosity, equation of state for the fluid, energy transport, momentum transport, and interaction with the fracturing solid domains, which is done through a novel immersed boundary approach. The solver is based on the governing equations being resolved using different control volume schemes, with discretization errors of either third, second, or first order. The solver is fully explicit and conditionally stable with a time step that is synchronized with the FDEM’s time step.

A fluid–structure interaction (FSI) methodology is presented for simulating elastic bodies embedded and/or encapsulating viscous incompressible fluid. The fluid solver is based on finite volume and the large eddy simulation approach to account for turbulent flow. The structural dynamic solver is based on the combined finite element method–discrete element method (FEM-DEM). The two solvers are tied up using an immersed boundary method (IBM) iterative algorithm to improve information transfer between the two solvers. The FSI solver is applied to submerged vegetation stems and blades of small-scale horizontal axis kinetic turbines. Both bodies are slender and of cylinder-like shape. While the stem mostly experiences a dominant drag force, the blade experiences a dominant lift force. Following verification cases of a single-stem deformation and a spinning Magnus blade in laminar flows, vegetation flexible stems and flexible rotor blades are analysed, while they are embedded in turbulent flow. It is shown that the single stem’s flexibility has higher effect on the flow as compared to the rigid stem than when in a dense vegetation patch. Making a marine kinetic turbine rotor flexible has the potential of significantly reducing the power production due to undesired twisting and bending of the blades. These studies point to the importance of FSI in flow problems where there is a noticeable deflection of a cylinder-shaped body and the capability of coupling FEM-DEM with flow solver through IBM.

From its inception, the combined finite discrete element method has used a distributed potential contact force algorithm to resolve interaction between finite elements. The contact interaction algorithm relies on evaluation of the contact force potential field. The problem with existing algorithms is that the potential field introduces artificial numerical non-smoothness in the contact force. This work introduces a smooth potential field based on the finite element topology, and a generalized contact interaction law is constructed on top of the smooth potential field. A number of validation cases for the proposed algorithm, considering different shapes of discrete elements, are presented, and detailed aspects of the proposed contact interaction law are tested with numerical examples.

Theoretical analysis and nowadays advanced numerical simulations for bedload particle transport widely share a popular assumption: All sediments are spherical and can be simplified as spheres, which apparently differs from reality. In order to explore the shape effects of sediment particles on their transport and to find out the possible consequence originated from the spherical assumption, a particle resolved computational model is established by combining the large eddy simulation for fluid and the discrete element method for the solid particles using an immersed boundary (IB) technique. Using this model, simulations are conducted for spherical and non-spherical bedload particles in both laminar and turbulent open channel flows. Simulation results show that shape of sediment particles has direct influence on the incipient motion in both laminar and turbulent flows. In laminar flows, the widely adopted spherical particles tend to exhibit over 5 times higher traveling speed compared with the non-spherical particles, and over 4 times longer time lag during incipient motion. In turbulent flows, the disk-shaped non-spherical particle yields up to 60% higher travel speed, 50% larger saltation height and 126% longer saltation length compared with spherical particles. The travel modes of non-spherical sediment particles during incipient motion are also analyzed.