| The objective of this work is to develop a novel, mesoscopic-based, computational fluid dynamics (CFD) methodology for the simulation of multi-phase flows within complex ge- ometries. Rooted in kinetic theory, this scheme, called the spectral-element discontinuous Galerkin lattice Boltzmann method (SEDG-LBM), solves the lattice Boltzmann equations (LBE) on non-uniform grids. A numerical framework, based on the SEDG method, is de- signed to extend the capabilities of the lattice Boltzmann method (LBM) to body-fitting, unstructured hexahedral elements. As a result, the scheme is able to investigate multiphase flows for a variety of complex geometries while retaining the simple implementation inherent in the LBM. Able to run on over 100, 000 processors, this algorithm achieves high levels of scalability and has the potential to tackle difficult engineering problems associated with current and future generations of nuclear energy systems.;Originally developed for isothermal single-phase fluid flows, the SEDG-LBM is augmented to simulate multi-phase (liquid-gas & liquid-liquid) flow and passive-scalar heat transfer for single-phase flows. A novel solution procedure based on the Strang splitting method is pre- sented which succesfully eliminates parasitic currents. Numerical investigations for single- phase natural convection and conjugate heat transfer are also considered. Validation for several flow applications include natural convection within a square cavity and concentric annulus, conjugate heat transfer within a composite two-layer annulus, and conjugate natural convection heat transfer in a horizontal annulus. Future investigations of buoyancy-driven motion of viscous drops for low Reynolds number flow through periodically constricted cap- illaries are considered. Results based on the aforementioned applications suggest that the SEDG-LBM is a promising tool for investigating thermal phase-change phenomena in pres- surized water reactor (PWR) fuel assemblies. |
