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...[ Read more ]

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.