Application And Study On Numerical Algorithm Of The Boltzmann Model Equation In Channel Flow

Because of the complexity of the Boltzmann equation,there are not many numerical simulation methods directly based on Boltzmann equation or Boltzmann model equation for solving the problems in rarefied gas dynamics.Among these methods, the unified simplified kinetic numerical method that combines the discrete velocity ordinate method and finite difference method makes a great success,for this method can simulate all flow regimes from continuum to rarefied.In this paper, the veracity and the validity of this method in the flow simulation over the complete spectrum of flow regimes are studied. and the significant effects of the different numerical schmes for the calculation are analyzed,The principle for the choice of discrete velocities is investigated. And the implicit unified simplified kinetic numerical methods are designed for improving the computational efficiency.At the end, the application of this method for solving the two dimensional inner flow problems are presented.The thesis contains five chapters as follow:Chapter 1 is a preface,in which the numerical methods based on Boltzmann equation or its model are briefly reviewed. Through comparing the characteristics and limitations of different methods,the advancement of the unified simplified kinetic numerical method in the simulation of the flow over the all regimes is inteoduced. And at the end of this chapter,the major objectives of the present paper are presented.In chapter 2,The concept of the rarefied gas flow analyzed by different flow regime is built through ploting the flow regimes. The velocity distribution function with its governing equation-Boltzmann equation are introduced in brief,and the properties are studied in mathematical point And the unified kinetic equation from continuum flow to rarefied flow is built through modeling the molecular collision.keeping the maintain characters of the Boltzmann equation.In the third chapter,the principle of the discrete velocity ordinate method is presented.Through the velocity space discreted,the convective terms of the Boltzmann modle equation are linearized,and turned the infinite space into limited point,the problem is simplified.The different simplified velocity distribution functions are calculated by different numerical schemes first time in this issue.And the advantages of this method relative to the consistant method are analyzed through simulating the classical shock-wave tube problem.And in this chapter,a implicit scheme for one dimensional kinetic problem is developed.It's shown from the results that the computational time in the simulations of the high Mach number or rarefied transional flow regime is shorted by the implicit numerical method,because that the restricted relation between the computational time step and the stability condition is avoided.Alse the origin error fro this algorithm and the effective factors of the discreted velocities are analyzed.Chapter 4 starts the study of the implicit kinetic scheme for the two dimensional inner flow.Through the velocity discreted and the distribution function simplified,the governing equations for the simplified distribution functions under the discreted velocitiea are deveploed.Then the numerical equations using defferent explicit and implicit schemes for solving two dimensional problems are designed.At the same time,the various boundary conditions of the inner flow are described.The pressure boundary condition in DSMC method is introduced, and the numerical boundary matching the back flow pressure is developed The complete diffuse reflection model on the interaction of the molecules with solid surface is studied, also the model is simulated in numerical formula.Through thr simulations of the Poiseuille micro channel flow and the micro nozzle flow,and comparing the results of different kinetic discreted schmes with the literatures',the reliability of this method and the computational efficiency of the implicit schmes are arguedThe concluding remarks of the present paper and the foreground of the unified simplified kinetic numerical method are given in chapter 5.