Study Of The Gas Kinetic Scheme Based On The Analytic Solution Of Model Equations

Near space hypersonic vehicles have been a focus in recent years.These vehicles can cruise in the atmosphere with hypersonic velocities and also can reentry the atmosphere,thus have high military and civil values.Accurate prediction of its aerodynamic characteristics is very important.The conventional CFD techniques by solving Navier-Stokes equations with the non-slip or slip boundaries are not competent due to the wide working range,i.e.,about 20 km to 100 km.As a result,rarefied gas dynamics is needed.The Unified Gas Kinetic Scheme(UGKS)is based on the analytical solution of Boltzmann model equations and is valid for all flow regimes theoretically.The time step in UGKS is determined by CFL condition and not limited by the mean collision time.Moreover,it is free from statistical noise.However,its efficiency is very low and the computational cost is tremendous which restricts its application in practice.Aiming at the three dimensional complex applications in various regimes,UGKS and GKS are constructed and validated in this dissertation.The effect of whether or not the compatibility condition is satisfied on the result and computational efficiency is studied.A common rule for determining the evolving time step in implicit GKS is proposed and implicit UGKS is introduced.Finally,with the help of the MPI and OpenMP hybrid parallelization the flowfields around a two dimensional hypersonic vehicle and a 3D sphere and the X38 vehicle of NASA are simulated.The dissertation consists of seven chapters as follows:The first chapter is the introduction.The background is introduced firstly,and then the numerical methods for flows covering various regimes are outlined.The progress of GKS/UGKS made in the last two decades are emphasized.Finally,the dissertation content is summarized briefly.The GKS and UGKS methods are constructed and validated in the second chapter.The Boltzmann equation and several collision models are presented.The details for constructing the GKS and UGKS methods,the nondimensionalization method and the boundary conditions are given.The jet interaction on a reentry vehicle is simulated by the GKS method.The UGKS method is validated by simulating various flows including cavity,slit,wedge and cylinder,etc.The third chapter is about the compatibility condition in UGKS.A theoretic analysis of the numerical error introduced by numerical quadrature in UGKS is given.Conservative discrete ordinate method(CDOM)is introduced with which the compatibility condition can be satisfied at discrete level.In the fourth chapter,the efforts for improving the computational efficiency of the GKS and UGKS methods are summarized.Implicit GKS was implemented and a common rule for choosing the evolving time step in implicit GKS was given.By applying LU technique on the model equation,implicit UGKS was introduced.The factors affecting the parallel strategy and efficiency in UGKS are analyzed.A hybrid parallel code,which utilize MPI after decomposition of the physical space mesh and OpenMP in the velocity space loops,is devised.The computational efficiency of the hybrid method is compared with the MPI-only method.The fifth chapter is about the hypersonic flow around a blunt cone.The aerodynamic characteristics between 40 km and 90 km are simulated.The 2D UGKS was further validated by comparison with the DS2 V results.The distributions of macroscopic variables,including pressure,density,temperature,mean free path and local Knudsen number,and mesoscopic probability density function along the forward and backward axes and on the wall are analyzed.The sixth chapter is the three dimensional application.The high velocity flow fields around a sphere and the X38 vehicle are simulated and compared with experimental results.The computational cost was also given.The last chapter is the conclusion of the dissertation.