scholarly journals Hilbert Expansion of the Boltzmann Equation with Specular Boundary Condition in Half-Space

2021 ◽  
Author(s):  
Yan Guo ◽  
Feimin Huang ◽  
Yong Wang
Keyword(s):  
Boundary Condition ◽  
Boltzmann Equation ◽  
Half Space ◽  
The Boltzmann Equation ◽  
Hilbert Expansion

Bifurcation on boundary data for linear broadwell model with conservative boundary condition

2014 ◽  
Vol 11 (03) ◽  
pp. 603-619 ◽  
Author(s):  
Shijin Deng ◽  
Weike Wang ◽  
Shih-Hsien Yu
Keyword(s):  
Boundary Condition ◽  
Boltzmann Equation ◽  
Kinetic Model ◽  
Boundary Data ◽  
Diffuse Boundary ◽  
The Boltzmann Equation ◽  
Simple Kinetic Model ◽  
Physical Boundary

We study a simple kinetic model with a conservative boundary condition which resembles the Maxwell diffuse boundary condition for the Boltzmann equation. We use a streamlined approach to construct the global pointwise structure of the full boundary data from the imposed boundary condition. Our estimates are strong enough to conclude the bifurcation in terms of the coefficients of the Broadwell model and the speed of the physical boundary.

scholarly journals Stability estimates of the Boltzmann equation in a half space

2007 ◽  
Vol 65 (4) ◽  
pp. 653-682 ◽  
Author(s):  
Myeongju Chae ◽  
Seung-Yeal Ha
Keyword(s):  
Boltzmann Equation ◽  
Half Space ◽  
Stability Estimates ◽  
The Boltzmann Equation

scholarly journals Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

2017 ◽  
Vol 823 ◽  
pp. 511-537 ◽  
Author(s):  
Lei Wu ◽  
Henning Struchtrup
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Boltzmann Equation ◽  
Rarefied Gas ◽  
Thermal Slip ◽  
Thermal Transpiration ◽  
Rarefied Gas Flows ◽  
The Boltzmann Equation ◽  
Kinetic Boundary ◽  
Slip Coefficients

Gas–surface interactions play important roles in internal rarefied gas flows, especially in micro-electro-mechanical systems with large surface area to volume ratios. Although great progress has been made to solve the Boltzmann equation, the gas kinetic boundary condition (BC) has not been well studied. Here we assess the accuracy of the Maxwell, Epstein and Cercignani–Lampis BCs, by comparing numerical results of the Boltzmann equation for the Lennard–Jones potential to experimental data on Poiseuille and thermal transpiration flows. The four experiments considered are: Ewart et al. (J. Fluid Mech., vol. 584, 2007, pp. 337–356), Rojas-Cárdenas et al. (Phys. Fluids, vol. 25, 2013, 072002) and Yamaguchi et al. (J. Fluid Mech., vol. 744, 2014, pp. 169–182; vol. 795, 2016, pp. 690–707), where the mass flow rates in Poiseuille and thermal transpiration flows are measured. This requires that the BC has the ability to tune the effective viscous and thermal slip coefficients to match the experimental data. Among the three BCs, the Epstein BC has more flexibility to adjust the two slip coefficients, and hence for most of the time it gives good agreement with the experimental measurements. However, like the Maxwell BC, the viscous slip coefficient in the Epstein BC cannot be smaller than unity but the Cercignani–Lampis BC can. Therefore, we propose to combine the Epstein and Cercignani–Lampis BCs to describe gas–surface interaction. Although the new BC contains six free parameters, our approximate analytical expressions for the viscous and thermal slip coefficients provide useful guidance to choose these parameters.

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