THESIS
2013
xvii, 163 pages : illustrations (chiefly color) ; 30 cm
Abstract
With the discrete ordinate method, a multi-scale unified gas-kinetic scheme(UGKS)
for entire Knudsen number
flows has been constructed based on the kinetic
Shakhov model for monatomic gases and Rykov model for diatomic gases.
Instead of particle-based modeling for the rarefied
flow, such as the direct simulation
Monte Carlo (DSMC) method, the philosophical principle underlying the
current study is a partial-differential-equation (PDE)-based modeling. Since the
valid scale of the kinetic equation and the scale of mesh size and time step may
be different signicantly, the gas evolution in a discretized space is modeled with
the help of evolution solution of the kinetic model, instead of directly discretization
of the partial differential equation. Due to the use of both hydrod...[
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With the discrete ordinate method, a multi-scale unified gas-kinetic scheme(UGKS)
for entire Knudsen number
flows has been constructed based on the kinetic
Shakhov model for monatomic gases and Rykov model for diatomic gases.
Instead of particle-based modeling for the rarefied
flow, such as the direct simulation
Monte Carlo (DSMC) method, the philosophical principle underlying the
current study is a partial-differential-equation (PDE)-based modeling. Since the
valid scale of the kinetic equation and the scale of mesh size and time step may
be different signicantly, the gas evolution in a discretized space is modeled with
the help of evolution solution of the kinetic model, instead of directly discretization
of the partial differential equation. Due to the use of both hydrodynamic
and kinetic scales
flow physics in a gas evolution model at the cell interface, the
unified scheme can basically present accurate solution in all
flow regimes from
the free molecular to the Navier-Stokes solutions. To overcome the bottleneck of
massive memory requirement of discrete ordinate method, the adaptive method
in velocity space is developed for the simulation of hypersonic flows.
In comparison with the DSMC, the current method is much more efficient than
DSMC in low speed transition and continuum
flow regimes, and it has better capability than Navier-Stokes solver in the capturing of non-equilibrium flow
physics in the transition and rarefied
flow regimes. As a result, the current
method can be useful in the
flow simulation where both continuum and rarefied
flow physics needs to be resolved in a single computation.
In this thesis, we are going to extensively evaluate the performance of the unified
gas-kinetic scheme from free molecular to the continuum Navier-Stokes solutions,
and from low speed micro-flow to high speed non-equilibrium aerodynamics.
The simulation results will be compared with experimental measurements and
DSMC results. These numerical test cases clearly demonstrate that the unified
gas kinetic scheme is a reliable method for the rarefied flow computations, and
the scheme provides an important tool in the study of non-equilibrium flow.
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