The development of gas-kinetic theory based methods for non-equilibrium flow simulations

Abstract

Non-equilibrium flows are prevalent in diverse engineering applications and significantly influence heat and mass transfer. However, experimental investigations are often environmentally demanding and costly, underscoring the importance of developing numerical methods. Non-equilibrium physics can result from the free transport of gas molecules or from physical and chemical transformations. Accurately describing these phenomena requires additional degrees of freedom, as macroscopic information alone is insufficient. Therefore, a mesoscopic description using gas-kinetic theory is necessary. The unified gas-kinetic scheme (UGKS) and the unified gas-kinetic wave-particle method (UGKWP) are two prominent numerical methods based on gas-kinetic theory. By introducing degrees of freedom through deterministic discrete velocity space or stochastic particles, these methods capture the evolution of the gas distribution function, preserving the non-equilibrium physics of flow fields. The flux construction in both methods is based on the integral solution of the kinetic model, which couples particle collisions and free transport, thereby removing the restrictions on time step and mesh size imposed by traditional splitting methods. Consequently, the UGKS and UGKWP are capable of multiscale simulations across all flow regimes. In this study, these methods are further developed in terms of application, acceleration, and extension. The UGKWP is applied to non-equilibrium flow simulations in near-space environments, extended to account for vibrational non-equilibrium, and accelerated through adaptive wave-particle decomposition. For UGKS, an adaptive velocity space decomposition is employed to extend vibrational non-equilibrium with heat flux corrections, develop implicit acceleration techniques, and ultimately extend the scheme to chemical non-equilibrium. All research presented in this study has been validated through simulations ranging from classical one-dimensional cases to complex three-dimensional geometries. Overall, this study demonstrates the tremendous potential of gas-kinetic theory-based numerical methods for non-equilibrium flow simulations.

Date of Award	2024
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Kun XU (Supervisor)