使用极坐标格子玻尔兹曼方法研究冲击过程——复杂系统中非平衡效应的探索
Polar Coordinate Lattice Boltzmann Studying of Shocking Process——Investigation of Non-Equilibrium Effects in Complex System

DOI: 10.12677/CMP.2013.24012, PP. 88-96

Keywords: 格子玻尔兹曼方法；冲击波；非平衡效应
Lattice Boltzmann Method, Shock Wave, Non-Equilibrium Effects

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文使用极坐标高速可压格子玻尔兹曼模型研究冲击过程。其中离散速度模型是由Watari和Tsutahara提出的D2V97，对流项采用修正的Warming-Beam格式处理。分别模拟研究了冲击波在环形区域和圆形区域中向内传播过程中物理量的变化规律，并通过离散速度分布函数的速度矩分析了冲击波波阵面附近的非平衡效应。为了从更基本层面理解界面行为，给出了波阵面处真实分布函数在速度空间的示意图。

The Polar Coordinate Lattice Boltzmann (PCLB) model is used to investigate the shocking processes. The discrete velocity model used in this PCLB is the D2V97 presented by Watari and Tsutahara. The convective term is treated with a modified Warming-Beam scheme. Two shocking processes are investigated. In one case, the evolution of a shock wave travels inwards within an annular area is studied. In the other case, the evolution of a shock wave travels inwards within a circular area is studied. The non-equilibrium effects around the shock fronts are investigated by ana- lyzing the simulated results of velocity moments of local discrete distribution function. To further understand the inter- face from a more fundamental level, we give the sketch of the actual distribution function in velocity space around the shock front.

References

[1]	Succi, S. (2001) The Lattice Boltzmann Equation for Fluid Dy-namics and Beyond. Oxford University Press, New York.
[2]	许爱国, 张广财, 李华, 朱建士等. (2011) 材料动力学的介观模拟(北京应用物理与计算数学研究所讲义)[Z]. 北京.
[3]	Xu, A., Zhang, G., Gan, Y., Chen, F. and Yu, X. (2012) Lattice Boltzmann modeling and simulation of compressible flows. Frontiers of Physics, 7, 582-600.
[4]	Pan, X., Xu, A., Zhang, G. and Jiang, S. (2007) Lattice Boltz- mann approach to high-speed compressible flows. International Journal of Modern Physics C, 18, 1747-1764.
[5]	Gan, Y., Xu, A., Zhang, G. and Li, Y. (2008) Finite-difference Lattice Boltzmann scheme for high-speed compressible flow: Two-dimensional case. Communications in Theoretical Physics, 50, 201-210.
[6]	Gan, Y., Xu, A., Zhang, G., Yu, X. and Li, Y. (2008) Two-dimen- sional Lattice Boltzmann model for compressible flows with high mach number. Physica A, 387, 1721-1732.
[7]	Gan, Y., Xu, A., Zhang, G. and Li, Y. (2011) Flux limiter Lattice Boltzmann scheme approach to compressible flows with. Com- munications in Theoretical Physics, 56, 490-498.
[8]	Gan, Y., Xu, A., Zhang, G. and Li, Y. (2011) Lattice Boltzmann study on Kelvin-Helmholtz instability: Roles of velocity and density gradients. Physical Review E, 83, Article ID: 056704.
[9]	Chen, F., Xu, A., Zhang, G., Gan, Y., Tao, C. and Li, Y. (2009) Lattice Boltzmann model for compressible fluids: Two-dimen- sional case. Communications in Theoretical Physics, 52, 681- 694.
[10]	Chen, F., Xu, A., Zhang, G., Li, Y. and Succi, S. (2010) Multi- ple-relaxation-time Lattice Boltzmann approach to compressible flows with flexible specific-heat ratio and prandtl number. Eu- rophysics Letters, 90, Article ID: 54003.
[11]	Chen, F., Xu, A., Zhang, G. and Li, Y. (2010) Three-dimensional Lattice Boltzmann model for high-speed compressible flows. Communications in Theoretical Physics, 54, 1121-1128.
[12]	Chen, F., Xu, A., Zhang, G. and Li, Y. (2011) Multiple-relaxa- tion-time lattice Boltzmann model for compressible fluids. Phys- ics Letters A, 375, 2129-2139.
[13]	Chen, F., Xu, A., Zhang, G. and Li, Y. (2011) Flux limiter Lattice Boltzmann for compressible flows. Communications in Theo- retical Physics, 56, 333-338.
[14]	Chen, F., Xu, A., Zhang, G. and Li, Y. (2011) Prandtl number effects in MRT lattice Boltzmann models for shocked and un- shocked compressible fluids. Theoretical and Applied Mechan- ics Letters, 1, Article ID: 052004.
[15]	Chen, F., Xu, A., Zhang, G. and Li, Y. (2011) Multiple-relaxa- tion-time Lattice Boltzmann approach to Richtmyer-Meshkov. Communications in Theoretical Physics, 55, 325-334.
[16]	Gan, Y., Xu, A., Zhang, G. and Yang, Y. (2013) Lattice BGK kinetic model for high speed compressible flows: Hydrodynamic and nonequilibrium behaviors. EPL, 103, Article ID: 24003.
[17]	Chen, F., Xu, A., Zhang, G. and Wang, Y. (2013) Two dimen- sional MRT LB model for compressible and incompressible flows. Frontiers of Physics, in press. arXiv: 1305.4736.
[18]	Lin, C., Xu, A., Zhang, G., Li, Y. and Succi, S. (2013) Polar coordinate lattice Boltzmann modeling of compressible flows. e-print arXiv: 1302.7104.
[19]	Yan, B., Xu, A., Zhang, G., Ying, Y. and Li, H. (2013) Lattice Boltzmann model for combustion and detonation. Frontiers of Physics, 8, 94-110.
[20]	Lin, C., Xu, A., Zhang, G. and Li, Y. (2013) Polar coordinate lattice Boltzmann modeling of detonation phenomena. e-print arXiv: 1308.0653.
[21]	Watari, M. (2011) Rotational slip flow in coaxial cylinders by the finite-difference lattice Boltzmann methods. Communica- tions in Computational Physics, 9, 1293-1314.
[22]	Watari, M. (2010) Relationship between accuracy and number of velocity particles of the finite-difference lattice Boltzmann method in velocity slip simulations. Journal of Fluids Engineer- ing, 132, Article ID: 101401.
[23]	Watari, M. and Tsutahara, M. (2003) Two-dimensional thermal model of the finite-difference lattice Boltzmann method with high spatial isotropy. Physical Review E, 67, Article ID: 036306.

Full-Text