Numerical Study of Dynamic Phase Transitions in Shock Tube
-
摘要: 用松弛模型研究了范德瓦流体中的激波管问题．当松弛参数趋于0时模型存在一个确定的黎曼解．在数值方面推导了松弛格式（relaxing）和完全松弛格式（relaxed）．在一维问题中，对于不同的剖面，数值模拟显示结果趋向于黎曼解，在理论上和数值上研究了参数的影响．对于特定的初始激波剖面，观察到了非经典的反射波．在二维问题中，研究了曲面波前的数值演化，得到一些有趣的波斑图．Abstract: Shock tube problem of a Van der Waals fluid with a relaxation model was investigated. In the limit of relaxation parameter tending towards zero, this model yields a specific Riemann solver. Relaxing and relaxed schemes were derived. For an incident shock in a fixed tube, numerical simulations show convergence toward the Riemann solution in one space dimension. Impact of parameters was studied theoretically and numerically. For certain initial shock profiles, nonclassical reflecting wave was observed. In two space dimensions, the effect of curved wave fronts was studied, and some interesting wave patterns were exposed.
-
Key words:
- phase transition /
- shock /
- relaxation
-
[1] Baker G A.Quantitative Theory of Critical Phenomena[M].San Diego:Academic Press,1990. [2] Hsieh Dinyu,TANG Shao-qiang,WANG Xiao-ping.On hydrodynamic instabilities, chaos and phase transition[J].Acta Mech Sinica,1996,12(1):1-14. [3] Shu C W. A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting[J].J Comp Phys,1992,2（100）:424-429. [4] Hsieh Dinyu,WANG Xiao-ping.Phase transition in van der waals fluid[J].SIAM J Appl Math,1997,57(4):871-892. doi: 10.1137/S0036139995295165 [5] Slemrod M.Admissibility criteria for propagating phase boundaries in a van der Waals fluid[J].Arch Rat Mech Anal,1983,4（81）:301-315. [6] JIN Sin,XIN Zhou-ping.The relaxation schemes for systems of conservation laws in arbitrary space dimensions[J].Comm Pure Appl Math,1995,48(3):235-278. doi: 10.1002/cpa.3160480303 [7] Natalini R,TANG Shao-qiang. Discrete kinetic models for dynamic phase transitions[J].Comm Appl Nonlinear Anal,2000,7(2):1-32. [8] TANG Shao-qiang, WANG Ping. Pattern formation in dynamic phase transitions[J].Chin Phy Lett,2004,21(8):1566-1568. doi: 10.1088/0256-307X/21/8/043 [9] TANG Shao-qiang,ZHAO Hui-jiang.Stability of Suliciu model for phase transitions[J].Comm Pure Appl Anal,2004,3（4）:545-556. doi: 10.3934/cpaa.2004.3.545 [10] 王平，唐少强.松驰模型中液气共存平衡态[J].应用数学和力学，2005,26(6):707-713. [11] Fornberg B, Witham G B.A numerical and theoretical study of certain nonlinear wave phenomena[J].Philos trans Roy Soc London Ser A,1978,289:373-404. doi: 10.1098/rsta.1978.0064 -
计量
- 文章访问数: 2875
- HTML全文浏览量: 167
- PDF下载量: 621
- 被引次数: 0
下载:
渝公网安备50010802005915号