The Boltzmann equation can describe the gas transport phenomena for the full spectrum of flow regimes and act as the main foundation for the study of complex gas dynamics including spacecraft re-entering Earths atmosphere.However,the difficulties encountered in solving the full Boltzmann equation are mainly associated with the nonlinear multidimensional integral nature of the collision term,and an exact solution of the Boltzmann equation is impractical for the analysis of practical complex flows.From the kinetic-molecular theory of gases,numerous statistical or relaxation kinetic model equations resembling various order of moments of the original Boltzmann equation have been put forward.In this work,instead of solving the full Boltzmann equation,it can be indicated that a unified computational modeling based on the Boltzmann equation has been presented in describing flow transport phenomena around complex bodies in various flow regimes,and the theory and computational techniques of a gas-kinetic unified algorithm(GKUA)have been established and used to simulate the reentry aerodynamics from highly rarefied free-molecular one to continuum regimes with the development of massive parallel implementation.Based on the collision relaxation spacing theory of the Boltzmann equation,the unified Boltzmann model equation for describing the complex multi-scale flows covering various flow regimes can be deduced,in which the unified expressions on the molecular collision relaxing parameter and the local equilibrium distribution function are presented by computable modeling of the collision integral of the Boltzmann equation for the full spectrum of flow regimes.The unified expressions are integrated with the macroscopic flow variables,the gas viscosity transport coefficient,the thermodynamic effect,the molecular power law,molecular models,and the flow state controlling parameter from various flow regimes.The gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by using the discrete velocity ordinate(DVO)technique and the unsteady time-splitting method.The discrete velocity numerical integration method is developed to evaluate the macroscopic flow parameters at each point in the physical space.The computing principle of domain decomposition is investigated on the basis of two-phase six-dimensional space of physical space and velocity space,and then the computing technique of parallel domain decomposition in the discrete velocity space is presented.As a result,the gas-kinetic massive parallel algorithm is developed to solve the hypersonic aerothermodynamics covering various flow regimes and the parallel speed-up almost goes up as near-linearity with the increase of the number of processors from 64~32768CPU and processor cores 500~45000 and 3125~112500 at least 88%parallel efficiency.To validate the accuracy and feasibility of the GKUA,the re-entering hypersonic flows past reusable spherical-cone satellite and spacecraft covering the whole of flow regimes are simulated.The computational results are found in good agreement with the related theoretical,DSMC,N-S,and experimental results.The computing practice has confirmed that the present gas-kinetic algorithm probably provides a promising approach for treating practical hypersonic flows during spacecraft re-entry from the gas-kinetic point of view of solving the Boltzmann model equation.