THESIS
2016
xiii, 123 pages : illustrations (some color) ; 30 cm
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 physic...[
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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.
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