TY - JOUR
T1 - NR𝑥𝑥 Simulation of Microflows with Shakhov Model
AU - Cai, Zhenning
AU - Li, Ruo
AU - Qiao, Zhonghua
N1 - Funding information:
^CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China ([email protected]). This author’s research was supported in part by the National Basic Research Program of China (2011CB309704), the National Science Foundation of China under grant 10731060, and NCET in China.
§ Institute for Computational Mathematics & Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). The work of this author was partially supported by Hong Kong RGC grant HKBU201710.
Publisher copyright:
© 2012 Society for Industrial and Applied Mathematics
PY - 2012/2/7
Y1 - 2012/2/7
N2 - In this paper, we propose a method to simulate the microflows with Shakhov model using the NR𝑥𝑥 method developed in [Z. Cai and R. Li, SIAM J. Sci. Comput., 32 (2010), pp. 2875- 2907; Z. Cai, R. Li, and Y. Wang, Commun. Comput. Phys., 11 (2012), pp. 1415-1438; Z. Cai, R. Li, and Y. Wang, J. Sci. Comput., to appear]. The equation under consideration is the Boltzmann equation with force terms, and the Shakhov model is adopted to achieve the correct Prandtl number. As the focus of this paper, we derive a uniform framework for different order moment systems on the wall boundary conditions, which is a major difficulty in the moment methods. Numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments.
AB - In this paper, we propose a method to simulate the microflows with Shakhov model using the NR𝑥𝑥 method developed in [Z. Cai and R. Li, SIAM J. Sci. Comput., 32 (2010), pp. 2875- 2907; Z. Cai, R. Li, and Y. Wang, Commun. Comput. Phys., 11 (2012), pp. 1415-1438; Z. Cai, R. Li, and Y. Wang, J. Sci. Comput., to appear]. The equation under consideration is the Boltzmann equation with force terms, and the Shakhov model is adopted to achieve the correct Prandtl number. As the focus of this paper, we derive a uniform framework for different order moment systems on the wall boundary conditions, which is a major difficulty in the moment methods. Numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments.
KW - Boundary conditions
KW - Microflow
KW - NRxx method
KW - Shakhov model
UR - http://www.scopus.com/inward/record.url?scp=84861404027&partnerID=8YFLogxK
U2 - 10.1137/110828551
DO - 10.1137/110828551
M3 - Journal article
AN - SCOPUS:84861404027
SN - 1064-8275
VL - 34
SP - A339-A369
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 1
ER -