Lin－Reissner－Tsien方程的自相似解

J·郝泽曼; K·法拉菲路; R·A·冯歌德

doi:10.3879/j.issn.1000-0887.2011.11.009

Lin－Reissner－Tsien方程的自相似解

doi: 10.3879/j.issn.1000-0887.2011.11.009

中佛罗里达大学数学系, 161364信箱, 奥兰多市, 佛罗里达州 32816-1364, 美国

详细信息

中图分类号: O175
计量
- 文章访问数: 1461
- HTML全文浏览量: 103
- PDF下载量: 735
- 被引次数: 0
出版历程
- 收稿日期: 2011-01-24
- 修回日期: 2011-07-08
- 刊出日期: 2011-11-15

Self-Similar Solutions to the Lin-Reissner-Tsien Equation

Department of Mathematics, University of Central Florida, P. O. Box 161364, Orlando, FL 32816-1364, USA

摘要

摘要: Lin－Reissner－Tsien方程描述了在跨音速近似下的不稳定跨音速流动．通过相似变换，将Lin－Reissner－Tsien方程简化为一个常微分方程．然后解析求解所得到的方程，并在某些情况下得到的正好是精确解．上述情况下无法得到精确解时，给出了数值模拟．还得到了行波解．
- Lin－Reissner－Tsien方程 /
- 自相似解 /
- 跨音速近似 /
- 非线性偏微分方程
Abstract: The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation.The equation was reduced to an ordinary differential equation via a similarity transformation. The resulting equation was then solved analytically,and in some cases even exactly.Numerical simulations were provided for the cases in which there were no exact solutions.Traveling wave solutions were also obtained.
- Lin-Reissner-Tsien equation /
- self-similar solutions /
- transonic approximation /
- nonlinear partial differential equation

HTML全文

参考文献(12)

[1]	Lin C C, Reissner E, Tsien H S. On two-dimensional non-steady motion of a slender body in a compressible fluid[J]. J Math Phys, 1948, 27: 220-231.
[2]	Ames W F, Nucci W N. Analysis of fluid equations by group methods[J]. J Eng Mech, 1985, 20(2): 181-187.
[3]	Kuz'min A G, Ivanova A V. The structural instability of transonic flow associated with amalgamation/splitting of supersonic regions[J]. Fluid Dynamics, 2004, 18(5): 335-344.
[4]	Bogdanov A N, Duesperov V N. The properties of asymptotic expansions for the parameters of unsteady transonic flow with axial symmetry[J]. Journal of Applied Mathematics and Mechanics, 2008, 72(1): 33-35. doi: 10.1016/j.jappmathmech.2008.03.009
[5]	Bibik Yu V, Duesperov V N, Popov S P. Structure of time dependent transonic flows in pane channels[J]. Fluid Dynamics, 2005, 40(2): 315-325. doi: 10.1007/s10697-005-0071-y
[6]	Glazatov S N. On solvability of a spatial periodic problem for the Lin-Reissner-Tsien equation of transonic gas dynamics[J]. Mathematical Notes, 2010, 87(1/2): 130-134. doi: 10.1134/S0001434610010177
[7]	Bogdanov A N, Duesperov V N. Higher approximations of the transonic expansion in problems of unsteady transonic flow[J]. Journal of Applied Mathematics and Mechanics, 1997, 61(5): 775-786. doi: 10.1016/S0021-8928(97)00101-9
[8]	Diesperov V N, Korolev G L. Triple-deck analysis of formation and evolution of supersonic zones and local separation zones in unsteady transonic flow over a surface roughness element[J]. Computational Mathematics and Mathematical Physics, 2005, 45(3): 516-523.
[9]	Bogdanov A N, Duesperov V N. Tollmien-Schlichting waves in a transonic boundary layer: excitation from the outer flow and from the surface[J]. Journal of Applied Mathematics and Mechanics, 2007, 71(2): 258-268. doi: 10.1016/j.jappmathmech.2007.06.009
[10]	Titov S S. A method finite-dimensional rings for solving nonlinear equations of mathematical physics[C] Ivanova T P. Aerodynamics. Saratov: Saratov University, 1988: 104-110. (in Russian)
[11]	Svirshchevskii S R. Lie-Bcklund symmetries of linear ODEs and generalized separation of variables in nonlinear equations[J]. Phys Lett A, 1995, 199(5/6): 344-348. doi: 10.1016/0375-9601(95)00136-Q
[12]	Polyanin A D, Zaitsev V F. Handbook of Nonlinear Partial Differential Equations[M]. Boca Raton: Chapman & Hall/CRC, 2004.