Numerical methods for granular media in multiphase fluids
(2025)
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- Abstract
- Immersed granular flows, which are mixtures of solid particles and interstitial fluid, are found in a wide range of natural and industrial processes, including landslides and sediment transport and fluidised beds. Modelling them is particularly challenging due to the complex interplay between solid contacts, fluid dynamics, and evolving interfaces. Numerical simulation is a powerful way of exploring such systems, providing detailed, time-resolved insights that are often difficult or impossible to capture experimentally. It enables key physical mechanisms to be isolated, hypotheses to be tested, and extreme conditions to be examined, making it a valuable complement to theoretical analysis and experimental work. This thesis focuses on the modelling of immersed granular flows across multiple regimes and scales. It begins with the challenge of simulating grains comparable in size to fluid discretisation within the Volume-Averaged Navier–Stokes (VANS) framework using an overlap-wise grain representation and semi-implicit time integration. These extensions enable simulation from coarse to fine discretisation and restore the flexibility of the Finite Element Method for handling complex geometries without mesh size restrictions. The model is extended further to include heat transfer, for which a new correlation is proposed for forced convection in granular suspensions. Spontaneous digging by a water droplet in a hot granular bed is investigated to reveal the main physical mechanisms involved. The model successfully reproduces the key phases of the digging process observed in experiments. Finally, the Particle Finite Element Method (PFEM) is employed to model immersed granular flows with free surfaces that are subject large deformations. This Lagrangian formulation enables domain motion and interface tracking to be handled robustly. The historical Lituya Bay landslide and tsunami are simulated to demonstrate the model's capabilities and fidelity to real-world phenomena. Overall, the framework provides a versatile tool for exploring complex, multiphase granular phenomena.
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Citations
Henry, M. (2025). Numerical methods for granular media in multiphase fluids.