Nonlinear acoustics and shock formation in lossless barotropic Green--Naghdi fluids
Nonlinear acoustics and shock formation in lossless barotropic Green--Naghdi fluids
复制标题
无损正压绿色-纳格迪流体中的非线性声学和激波形成
DOI：
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发表时间：
2016
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影响因子：
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通讯作者：
I. Christov
中科院分区：
文献类型：
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作者：
I. Christov
在所谓的绿色-Naghdi理论下，考虑了两类正压流体的无耗可压缩非经典流体运动方程：（i）理想气体和（ii）服从二次状态方程的液体。一个精确的减少方面的标量的声学潜力和（标量）的热位移实现。这些模型的单向流动的非线性声学方程的属性和简化。具体而言，这样的流量的方程组的控制系统保持双曲线的要求，导致的物理参数和/或模型的适用性的限制。在忽略控制方程中与马赫数平方成正比的项的基础上，提出了一种弱非线性模型，对非线性项不作进一步的近似或修正。冲击波形成通过加速波吹的数值研究在一维的上下文中使用高分辨率Godunov型有限体积方案，从而验证以前的分析结果的爆破时间和对比这些结果与相应的经典（欧拉，即，无损可压缩）流体。
The equations of motion of lossless compressible nonclassical fluids under the so-called Green--Naghdi theory are considered for two classes of barotropic fluids: ( i ) perfect gases and ( ii ) liquids obeying a quadratic equation of state. An exact reduction in terms of a scalar acoustic potential and the (scalar) thermal displacement is achieved. Properties and simplifications of these model nonlinear acoustic equations for unidirectional flows are noted. Specifically, the requirement that the governing system of equations for such flows remain hyperbolic is shown to lead to restrictions on the physical parameters and/or applicability of the model. A weakly nonlinear model is proposed on the basis of neglecting only terms proportional to the square of the Mach number in the governing equations, without any further approximation or modification of the nonlinear terms. Shock formation via acceleration wave blow up is studied numerically in a one-dimensional context using a high-resolution Godunov-type finite-volume scheme, thereby verifying prior analytical results on the blow up time and contrasting these results with the corresponding ones for classical (Euler, i.e. , lossless compressible) fluids.