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This thesis presents a two-phase liquid-solid numerical model using Smoothed Particle Hydrodynamics (SPH). The scheme is developed for multi-phase flows in industrial tanks containing sediment used in the nuclear industry for decommissioning. These two-phase liquid-sediments flows feature a changing interfacial profile, large deformations and fragmentation of the interface with internal jets generating resuspension of the solid phase. SPH is a meshless Lagrangian discretization scheme whose major advantage is the absence of a mesh making the method ideal for interfacial and highly non-linear flows with fragmentation and resuspension. Emphasis has been given to the yield profile and rheological characteristics of the sediment solid phase using a yielding, shear and suspension layer which is needed to predict accurately the erosion phenomena. The numerical SPH scheme is based on the explicit treatment of both phases using Newtonian and non-Newtonian Bingham-type constitutive models. This is supplemented by a yield criterion to predict the onset of yielding of the sediment surface and a suspension model at low volumetric concentrations of sediment solid. The multi-phase model has been compared with experimental and 2-D reference numerical models for scour following a dry-bed dam break yielding satisfactory results and improvements over well-known SPH multi-phase models. A 3-D case using more than 4 million particles, that is to the author’s best knowledge one of the largest liquid-sediment SPH simulations, is presented for the first time. The numerical model is accelerated with the use of Graphic Processing Units (GPUs), with massively parallel capabilities. With the adoption of a multi-phase model the computational requirements increase due to extra arithmetic operations required to resolve both phases and the additional memory requirements for storing a second phase in the device memory. The open source weakly compressible SPH solver DualSPHysics was chosen as the platform for both CPU and GPU implementations. The implementation and optimisation of the multi-phase GPU code achieved a speed up of over 50 compared to a single thread serial code. Prior to this thesis, large resolution liquid-solid simulations were prohibitive and 3-D simulations with millions of particles were unfeasible unless variable particle resolution was employed. Finally, the thesis addresses the challenging problem of enforcing wall boundary conditions in SPH with a novel extension of an existing Modified Virtual Boundary Particle (MVBP) technique. In contrast to the MVBP method, the extended MVBP (eMVBP) boundary condition guarantees that arbitrarily complex domains can be readily discretized ensuring approximate zeroth and first order consistency for all particles whose smoothing kernel support overlaps the boundary. The 2-D eMVBP method has also been extended to 3-D using boundary surfaces discretized into sets of triangular planes to represent the solid wall. Boundary particles are then obtained by translating a full uniform stencil according to the fluid particle position and applying an efficient ray casting algorithm to select particles inside the fluid domain. No special treatment for corners and low computational cost make the method ideal for GPU parallelization. The models are validated for a number of 2-D and 3-D cases, where significantly improved behaviour is obtained in comparison with the conventional boundary techniques. Finally the capability of the numerical scheme to simulate a dam break simulation is also shown in 2-D and 3-D.

A new smoothed particle hydrodynamics (SPH) scheme is presented to simulate multi-component fluid mixing with thermally-driven buoyancy and temperature-dependent viscosities. The scheme is developed for multi-phase flows in industrial tanks used in the vitrification process in the nuclear industry for waste immobilisation before long-term storage. These multi-component flows feature a mixing of high-temperature phases composed of molten glass and highly radioactive waste, with fluid properties changing with temperature. SPH is a meshless Lagrangian discretization scheme whose major advantage is the absence of a mesh, making the method ideal for highly non-linear flows with mixing of multiple components whose properties change with time. Emphasis has been given to modelling the thermally-induced buoyancy flows from the external heating and viscous flow instabilities, which are needed to predict accurately the mixing phenomena. The numerical SPH scheme includes temperature-dependent viscosities, thermal conduction and convection using a Boussinesq approximation, and external heating. A new boundary treatment has been developed to implement adiabatic boundary conditions by extending the recently developed modified dynamic boundary condition (mDBC) to thermally-driven driven flows. The SPH scheme has been implemented to run on a graphics processing unit (GPU), showing speed-ups on the order of 50 compared to optimised code on a multi-core multi-thread central processing unit (CPU). The code is extensively validated for a range of test cases including two-phase Poiseuille flow where each phase has a different viscosity, temperature dependent Poiseuille flow, two-phase lid-driven cavity flow, and a differentially-heated cavity in 2-D and 3-D.For the two-phase Poiseuille flow, an interfacial instability is observed for certain ranges of viscosity and channel-width ratios. Both stable and unstable flow regimes are correctly predicted. The instability growth rate predicted by the new SPH model agrees with linear analytical theory, which has not been seen before. The evolution of consequent non-linear flow is straightforwardly predicted, with the interface remaining clear. A new mixing measure is proposed based on the combination of the finite time Lyapunov exponent (FTLE) and the volume fraction (VF) that enables both the degree of mixing at a point and how well-mixed the two phases are at that location to be quantified in a single value. The VF-FTLE mixing measure is applied to the two-phase lid-driven cavity flow, highlighting regions with high particle movement and where both phases are present. A new global mixing measure is established from this local measure, quantifying the change in overall mixing with time. The new model is applied to a vitrification melter for single-phase and two-phase flows with temperature-dependent viscosities. The VF-FTLE measure is applied to interpret the mixing taking place due to buoyancy-driven circulation within the heated melter. A 3-D flow instability is observed, likely related to a thin thermal boundary layer existing at high Rayleigh and Prandtl numbers, suggesting distinct flow regimes in the melter which requires further investigation.