An exact solution for finite‐amplitude plane sound waves in a dissipative fluid
An exact solution for finite‐amplitude plane sound waves in a dissipative fluid
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耗散流体中有限振幅平面声波的精确解
DOI：
10.1121/1.2026598
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发表时间：
1988
影响因子：
2.4
通讯作者：
H. Mitome
中科院分区：
文献类型：
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作者：
H. Mitome
有限振幅平面声波在耗散流体中的传播可以用Burgers方程描述，并得到其精确解。本文推导出了适合于时域波形直接数值计算的声压精确解。数值结果表明，该解描述了激波形成和衰减的整个传播过程。计算极限是结合计算系统确定的。计算结果表明，对于D0>0.0114和任意X值，都可以用本系统进行计算，其中D0表示耗散相对于非线性的重要性，X是由无损激波形成距离归一化的距离。还发现，D0极限值的解与X3.5的Fubini解平滑地连接。由于目前的解决方案是准确的，并产生在任何距离的波形，而不引入傅里叶级数…
The propagation of finite‐amplitude plane sound waves in a dissipative fluid can be described by Burgers’ equation, and its exact solution obtained. In this paper, an exact solution for the sound pressure, which is suitable for direct numerical computation of the waveform in the time domain, is derived. Numerical results illustrate that this solution describes the entire propagation process, including shock formation and decay. Computation limits are determined in connection with the computational system. It is found that computation is possible for D0>0.0114 and any value of X with the present system, where D0 indicates the importance of dissipation relative to nonlinearity and X is distance normalized by the lossless shock formation distance. It is also found that the solution for the limiting value of D0 connects smoothly with the Fubini solution for X 3.5. Since the present solution is exact and yields the waveform at any distance without introducing the Fourier serie...