| According to the requirements of the NSFC Project (Grant No. 19772018) and (Grant No. 19902021) and the National 863 Program (Grant No.2002AA726050), and based on the investigation of models and algorithms about inhomogeneous and non-equilibrium flows, two typical kinds of these flows: gas-solid two-phase flows and thermal chemical non-equilibrium gas flows, are chosen to study the properties of compressible inhomogeneous and non-equilibrium flows which are governed by the Boltzmann equation for trying to find the feasible models and numerical methods to solve these complicated flow problems.Firstly, the two-fluid model and the unified governing equations for dense compressible gas-solid flows are established on the concept of granular temperature which is used to represent the properties of this flow. Approximate Riemann solver of solid phase is deduced from the characteristics of wave propagating in the varied conditions including the vacuum, and the algorithm of Roe's fractional step scheme is constructed to solve non-isentropic dense compressible gas-solid flows. Numerical simulation of the shock-induced fluidization of inert powder layers is performed, the results show the detailed structure and the evolving process of the flow field. It is also experimentally proved that the model and the algorithm are valid, so the work of this paper can supply an effective method to describe the dense compressible two-phase flow with strong discontinuity surfaces.Secondly, analyzing the properties of gas-solid flow in the transitional region of rarefied gas and the requirements of the direct simulation Monte Carlo (DSMC) method, the relationship is set up between the gas-solid interaction based on the macro physical parameters and the single simulation particle's kinetic states via the micro-expression of the macro physical parameters, each coherent velocity distribution function of gas phase and solid phase is given in the unified form. The mechanical and thermal models of gas-solid interaction and the models of particle-particle collision are also constructed. The numerical disposition of the boundary conditions of solid phase is performed in the form of the granular temperature. Numerical solutions are obtained for the case of gas-solid transverse jet from a two-dimensional flat plate interacting with rarefied external hypersonic flows. As the more real model can be easily inducted to the DSMC method for solving physical chemical flow due to the physical simulation essence of the DSMC method, the work of this paper may provide a new approach to describe the gas-solid flow with chemical reactions in the transitional region.Thirdly, considering the particle simulation essential characteristics of the DSMC method and the equilibrium particle simulation method (EPSM), and each advantage and disadvantage in simulating mixed rarefied and continuum flows, the local Knudsen number Kn and Bird'sbreakdown parameter P are adopted as the physical and numerical criteria that identify the boundary between continuum and rarefied computational domains. Rationality that the DSMC method is implemented in rarefied region, and the EPSM method in continuum region is verified, the hybrid DSMC/EPSM code is presented to automatically divide zones in continuum/rarefied flows using the controlling parameters Kn and P. Simulations are performed for the cases of transverse jet from two-dimensional flat plate with non-thickness and thickness, inverse jet from flat-nosed cylinder interacting with rarefied external flows. The structure of flow field and the aerodynamic properties along with the varied Knudsen number and jet Mach number are analyzed in details, and the rarefied gas effects of the jet interaction are embodied in the transitional region.Lastly, the EPSM code, that is initially only used for integral degrees of free...
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