Developing a unified numerical scheme capable of accurately modeling flow physics across all flow regimes is a formidable and complex task. In the context of gas-particle systems, the gas phase is always in the hydrodynamic regime, whereas the solid particle flow exhibits multi-scale characteristics, from the hydrodynamic wave interaction in the continuum flow regime to the particle’s free transport in the collisionless regime, and it varies based on the particle phase’s Knudsen number (Kn). In this thesis, the multi-scale framework based on the gas-kinetic scheme (GKS) and unified gas-kinetic wave-particle method (UGKWP) is developed for the dilute and dense gas-particle system. Specifically, the GKS-UGKWP seamlessly transitions between an Eulerian-Eulerian method in the regime of inte...[ Read more ]

Developing a unified numerical scheme capable of accurately modeling flow physics across all flow regimes is a formidable and complex task. In the context of gas-particle systems, the gas phase is always in the hydrodynamic regime, whereas the solid particle flow exhibits multi-scale characteristics, from the hydrodynamic wave interaction in the continuum flow regime to the particle’s free transport in the collisionless regime, and it varies based on the particle phase’s Knudsen number (Kn). In this thesis, the multi-scale framework based on the gas-kinetic scheme (GKS) and unified gas-kinetic wave-particle method (UGKWP) is developed for the dilute and dense gas-particle system. Specifically, the GKS-UGKWP seamlessly transitions between an Eulerian-Eulerian method in the regime of intense particle collisions and an Eulerian-Lagrangian formulation in the collisionless regime. The UGKWP can effectively capture particle non-equilibrium transport during the intermediate transition regime, achieving a smooth shift between the Eulerian and Lagrangian limiting formulations, which is accomplished by weighting the mass distributions with respect to the local cell’s Kn number, employing exponential functions of the form e^−1/Kn for wave and (1 − e^−1/Kn) for discrete particles. The GKS-UGKWP successfully captures phenomena such as non-equilibrium particle trajectory crossings, bubble formation, particle clustering, and characteristic heterogeneous flow structures in fluidized beds. The statistical results obtained from the simulations agree well with experimental data. Furthermore, the GKS-UGKWP method is extended to poly-disperse gas-particle systems using the multi-fluid strategy. Consequently, even in multi-disperse systems with significant variations in physical properties (e.g., particle diameter, material density, etc.), each particle phase can adopt an optimal strategy for wave and particle decomposition, balancing physical accuracy and numerical efficiency. In addition, considering radiative transport systems, the transport of photons also exhibits multi-scale behavior, with the flow regime determined by the opacity of the background material. In this thesis, a multi-scale method based on UGKWP is developed for frequency-dependent radiation transport equations, and it can recover the photon’s free transport and thermal diffusion process in the limiting optically thin and thick regimes, respectively.