There is an increasing demand for multi-scale modeling and simulation of gas flows in various engineering applications, such as the re-entry of space shuttle and heat flow in micro devices. The unified gas-kinetic scheme (UGKS) is a newly developed multi-scale method to study gas flows in all Knudsen regimes from the continuum Navier-stokes solutions to the rarefied non-equilibrium transport. The main objective of this thesis research is to further develop UGKS and apply it to the study of multiple scale transport problems. In this thesis, the UGKS and its simplified variation - discrete unified gas-kinetic scheme (DUGKS) — are presented and several numerical examples are provided to validate the schemes. UGKS is further constructed for multi-component gas flow and is validated through the simu...[ Read more ]

There is an increasing demand for multi-scale modeling and simulation of gas flows in various engineering applications, such as the re-entry of space shuttle and heat flow in micro devices. The unified gas-kinetic scheme (UGKS) is a newly developed multi-scale method to study gas flows in all Knudsen regimes from the continuum Navier-stokes solutions to the rarefied non-equilibrium transport. The main objective of this thesis research is to further develop UGKS and apply it to the study of multiple scale transport problems. In this thesis, the UGKS and its simplified variation - discrete unified gas-kinetic scheme (DUGKS) — are presented and several numerical examples are provided to validate the schemes. UGKS is further constructed for multi-component gas flow and is validated through the simulations of shock structures at different Mach numbers and micro-channel flows driven by small pressure, temperature, and concentration gradients. Then UGKS is used to study the physics of low-speed micro-flows which include the sound-wave propagation and the cross-coupling phenomenon in micro-channel. In the study of sound-wave propagation, the phase speed and attenuation coefficient are extracted from the simulation under a wide range of Knudsen numbers from the continuum flow regime to the free molecular one. The comparison with the experiments shows good agreement in all Knudsen regimes. And the cross-coupling of thermal-osmosis and mechano-caloric effect in slightly non-equilibrium gas is simulated and analyzed for micro-channel with planner and ratchet surfaces. The variation of cross-coupling coefficient as a function of Knudsen number is obtained. At the same time, preliminary optimization for this kind of Knudsen pump is included.