On the robust, flexible and consistent implementation of time domain impedance boundary conditions for compressible flow simulations
On the robust, flexible and consistent implementation of time domain impedance boundary conditions for compressible flow simulations
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DOI：
10.1016/j.jcp.2016.03.010
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发表时间：
2016-06
期刊：
影响因子：
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通讯作者：
S. Jaensch;C. Sovardi;W. Polifke
中科院分区：
文献类型：
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作者：
S. Jaensch;C. Sovardi;W. Polifke
可压缩流的精确模拟需要对边界处声波的反射进行适当的模拟。本文讨论了时域阻抗边界条件（TDIBC）。所提出的公式允许在流入和流出边界施加所需的反射系数。我们的公式是众所周知的纳维-斯托克斯特征边界条件的扩展。边界处的频率相关反射用时域的状态空间模型实现。我们对如何构建和解释这种状态空间模型进行了全面的讨论。这个讨论表明，状态空间描述可以实现健壮和灵活的实现。它允许考虑复杂的反射系数，并以直接的方式考虑非恒定的CFD时间步长。此外，我们通过解析和数值证明了所提出的公式是一致的，即只要冲击边界的波是平面的，该公式就能保证流动模拟准确地显示所施加的反射系数，并且它禁止了平均流动变量的漂移。最后，成功地测试了层流和湍流的边界条件。
The accurate simulation of compressible flows requires the appropriate modeling of the reflection of acoustic waves at the boundaries. In the present study we discuss time domain impedance boundary conditions (TDIBC). The formulation proposed allows to impose a desired reflection coefficient at the inflow and outflow boundaries. Our formulation is an extension of the well known Navier–Stokes characteristic boundary conditions. The frequency dependent reflections at the boundaries are implemented with a state-space model in the time domain. We provide a comprehensive discussion on how such state-space models can be constructed and interpreted. This discussion shows that the state-space description allows a robust and flexible implementation. It allows to consider complex reflection coefficients and account for non-constant CFD time steps in a straight forward manner. Furthermore, we prove analytically and demonstrate numerically that the formulation proposed is consistent, i.e. the formulation ensures that the flow simulation exhibits the reflection coefficient imposed accurately, as long as the waves impinging on the boundary are plane, and it prohibits drift of the mean flow variables. Finally, the boundary conditions are tested successfully for laminar and turbulent flows.