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应用数学学报  1984, Vol. 7 Issue (4): 498-504    DOI:
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关于平面定常位势流中的声速线
管楚洤
中国科学院数学研究所
SONIC LINE IN A STEADY PLANE POTENTIAL FLOW
Guan Chu-quan
Institute of Mathematics, Academia Sinica
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摘要 Ringleb求得的光滑跨声速流动的特解[1]表明:声速并不是连续、等熵加速或减速气流的理论障碍,也就是说声速线不一定是奇线,流动可以光滑地通过声速线.另一方面,Morawetz[2]证明了光滑跨声速绕流没有邻近解,只是一种例外情况.[3]中曾证明了在某些情况下,连续跨声速流动存在具有弱击波的扰动解,声速线变为弱激波线,这些都表明声速线具有某些特殊的性质.
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管楚洤
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Abstract: In this paper some properties of the sonic line in a steady plane potential flow are discussed. We prove that if the flow is supersonic on both sides of a sonic line, then the sonic line is straight and the flow on either side must be a constant flow or simple waves. Moreover, we prove that under certain circumstances a sonic line in a continuous transonic flow will become a weak shock due to the effect of small disturbances.
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收稿日期: 1982-11-19;
引用本文:   
管楚洤. 关于平面定常位势流中的声速线[J]. 应用数学学报, 1984, 7(4): 498-504.
Guan Chu-quan. SONIC LINE IN A STEADY PLANE POTENTIAL FLOW[J]. Acta Mathematicae Applicatae Sinica, 1984, 7(4): 498-504.
 
[1] R.Courant and K.O.Fciedrichs,Supersonic Flow and Shock Waves.New York,1948,255-256.
[2] C.S.Morawetz,On the non-existence of continuous transonic flow past profiles,I,Comm.Pure Appl.Math.,9(1956),45-68.
[3] 管楚拴,连续跨声速流的扰动解,全国第二届跨音速流讨论会报告,1983年5月.
[4] Л.Д.朗道,E.M.果弗席兹,彭旭麟译,连续介质力学,第二册,人民教育出版社,1960年,562-574.
[5] 郭永怀,W.R.Sears,平面亚声速及跨声速位势流.高速空气动力学理论(W.R.Sears编)第六部分(F),国防工业出版社,1960年,595-597.
[6] A.A.Nikolsky and G.I.Taganov,Flow of Gas in A Local Supersonic Zone and Some Conditions for the Breakdown of Potential Flow,Prikladnaya Matematikai Mechanika,10(1946),481-502.
[7] Jameson,Numerical Solution of Nonlinear Partial Differential Equation of Mixed Type.Numeri-Solution of Partial Differential Equations-Ⅲ SYNSPADE(1975) ed.B.Hubbard,1976,275-320
[8] K.Y.Fung.,H.Sobiozky and R.Seebass,Shock-free Wing Design,A.I.A.A.Journal 18: 10(1980),1153-1158.
[9] C.S.Morawetz,The Mathematical Approach to the Sonic Barrier.Bull.Amer.Math.Soc.,6: 2(1982),127-145.
[10] E.Koppe and G.Meier,Exfahrungen mit optischen Methoden bei der Untersuchung transonischer Strömungen,Jahrgang,5(1965),150-157.
[11] L.Bers,Mathematical Aspects of Subsonic and Transonic Gas Dynamics,Surveys in Appl.Math.III,1958.
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