Unified gas-kinetic scheme for the study of multi-scale flows

Abstract

In the field of computational fluid dynamics (CFD), the multi-scale methods are constantly demanded for both engineering application and scientific research. The unified gas-kinetic scheme (UGKS) is a direct modeling on the numerical cell size and time step, which preserves the flow dynamics continuously from rarefied regime to continuum one. In this thesis, the multiscale property of UGKS is analysed and validated by numerical test cases. By applying UGKS to the study of the permeability of porous media, we find the valid regime of the slip-corrected Navier-Stokes solutions and generalize the relationships between permeability and the Knudsen number. With the help of fast spectral algorithm, the full Boltzmann collision term is built into the UGKS which improves the physical consistency of the scheme in the highly non-equilibrium regime. The Boltzmann collision term is hybridized with the Shakhov model with a criterion related to the local time step and relaxation time. The scheme keeps the efficiency of UGKS in the continuum regime and accuracy in the rarefied one. Based on the multi-component kinetic model and Maxwell equations, the UGKS is extended to the plasma flow simulation. The current model focuses on the fully ionized plasma with ion and electron. Plasma flow regimes from Vlasov modeling to magnetohy-drodynamic equations can be recovered by the UGKS, which is validated by numerical test cases. The UGKS is also used as a reliable tool to study the physical problems in the transitional regimes, such as the magnetic reconnection. The results are compared with other methods.

Date of Award	2016
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology