Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation

1996 ◽  
Vol 135 (1) ◽  
pp. 61-105 ◽  
Author(s):  
Jian-Guo Liu ◽  
Zhouping Xin
Keyword(s):  
Boundary Layer ◽  
Boltzmann Equation ◽  
Nonlinear Model ◽  
Fluid Dynamic ◽  
Layer Behavior ◽  
Model Boltzmann Equation ◽  
Fluid Dynamic Limit

Numerical solutions of the nonlinear model Boltzmann equations

1995 ◽  
Vol 448 (1932) ◽  
pp. 55-80 ◽  
Keyword(s):  
Boltzmann Equation ◽  
Nonlinear Model ◽  
Hyperbolic Conservation Laws ◽  
Numerical Solutions ◽  
Rarefied Gas ◽  
Operator Splitting ◽  
Time Integration ◽  
Physical Space ◽  
Rarefied Gas Flows ◽  
Model Boltzmann Equation

A time marching high resolution finite difference method is presented for obtaining numerical solutions of the nonlinear model Boltzmann equation for rarefied gases. The velocity space dependency of the distribution function is first discretized via the discrete ordinate method which renders the model Boltzmann equation in phase space to a set of non-homogeneous hyperbolic conservation laws in physical space. Then a high order characteristics-based essentially nonoscillatory method is extended and applied to solve them and resulting an accurate and oscillation free method for solving rarefied gas flows. The time integration of equations is done using operator splitting. The method is tested for the classical Riemann shock-tube problem to demonstrate its use and accuracy. Applications to practical rarefied gas dynamical problems including truly nonstationary shock wave diffraction around and steady supersonic flow over a circular cylinder are given. It is found that complete flowfields including shock waves and contact surface are resolved well with minimal oscillations in the solution and accurate results are attainable. Comparisons of the calculated shock diffraction patterns with experimental interferogram and cylinder drag coefficients with experimental data show good agreement.

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