Gas-kinetic unified algorithm for aerodynamics covering various flow regimes by computable modeling of Boltzmann equation

Abstract

The gas-kinetic unified algorithm (GKUA), to solve the modeling of the Boltzmann equation, has been developed to study the aerothermodynamics problems with the effects of wall activation energy covering various flow regimes. The unified velocity distribution function equation could be accordingly presented on the basis of the Boltzmann–Shakhov model. To remove the dependence of the distribution function on velocity space, the conservational discrete velocity ordinate method has been developed for hypervelocity flows. The gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by the operator splitting technique. The discrete velocity numerical integration method with the Gauss-type weight function has been developed to evaluate the macroscopic flow variables. Specially, to model the real physical process between gas molecules and the surface, the Maxwell-type gas-surface interaction model has been presented by the MD (molecular dynamic) simulation to obtain the energy adaptability coefficient. The multi-processing domain decomposition strategy and parallel implementation of high parallel efficiency and expansibility designed for the gas-kinetic numerical method is presented with good load balance and data communication efficiency. To validate the accuracy and feasibility of the present algorithm, the supersonic flows past two-dimensional circular cylinder are simulated covering various flow regimes. The results are in good agreement with the related theoretical, DSMC (Direct Simulation Monte Carlo), N–S (Navier–Stokes), and experimental data. The hypersonic reentry flows with the effects of wall activation energy around the Tianzhou-5 cargo spacecraft are simulated by the present GKUA and the massive parallel strategy. It has been confirmed that the present algorithm from the gas-kinetic point of view probably provides a promising approach to resolve the hypersonic aerothermodynamic problems with the complete spectrum of flow regimes during the re-entry and disintegration of the large-scale spacecraft.