简单波的解析解
Analytic Solutions of Simple Waves
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摘要: Riemann于1860年给出了简单波的一般解,可是欲将其中所含的一个任意函数的具体形式按边界条件或初始条件求出来,却难以实现,因而对具体问题就难以深入探讨.本文按拟线性偏微分方程的几何理论,十分方便地给出了由边界条件或初始条件所确定的简单波解析解,并用这些解讨论了有关流动的性质,且得到了若干新颖的结果Abstract: B. Riemann furnished the general solution of simple waves in 1860[1]. But it is difficult to find out the exact forms of the arbitrary function contained in the general solution which must satisfy boundary or initial conditions. For this reason it is inconvenient to probe into the characteristics of concrete problems. In this paper the analytic solutions of simple waves are afforded according to the geometric theory of quasi-linear partial differential equation, and they are determined with boundary or initial conditions. By using these solutions the specific properties of certain flows are discussed and novel results are obtained.
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Key words:
- simple waves /
- analytic solutions /
- discontinuity
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[1] Riemann,B,.Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite,Abhandlungen der Gessellschaft der Wissensehaften zu Göttingen,Mathem atisch-physikalische Klasse,8(43)(1860). [2] Couranl,R.and K,O.Friedrichs,《超声速流与冲击波》,科学出版社,北京(1986),26,32. [3] Landau and Lifshitz,Fluid Mechanics,Beijing(1987),379. [4] Courant,R,and D Hilbcrt,,《学物理方法》,卷Ⅱ,科学出版社(7981),49-54. -
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