On Two-Dimensional Sonic-Subsonic Flow
On Two-Dimensional Sonic-Subsonic Flow
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发表时间：
2007
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通讯作者：
Gui-Qiang G. Chen;C. Dafermos;M. Slemrod;Dehua Wang
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作者：
Gui-Qiang G. Chen;C. Dafermos;M. Slemrod;Dehua Wang
针对可能包含驻点的二维定常无旋流的欧拉方程的声速 - 亚声速近似解，建立了一个补偿紧致性框架。建立紧致性只需粗略估计。由此可知，欧拉方程的亚声速无旋解集是紧致的；因此，在障碍物（如机翼）上具有声速点的流动可以实现为严格亚声速流序列的极限。此外，可以从近似解构造声速 - 亚声速流。然后，将紧致性框架扩展到非定常无旋流的欧拉方程的自相似解。
A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-dimensional Euler equations for steady irrotational flows that may contain stagnation points. Only crude estimates are required for establishing compactness. It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points over an obstacle, such as an airfoil, may be realized as limits of sequences of strictly subsonic flows. Furthermore, sonic-subsonic flows may be constructed from approximate solutions. The compactness framework is then extended to self-similar solutions of the Euler equations for unsteady irrotational flows.