在人体发音过程仿真中，考虑声道边界的动态变化以及气流的流动，可以更加准确、真实地模拟声波在声道中的传播。在处理带有移动边界的气动声学问题时，相比传统声道声学研究中广泛应用的网格方法，无网格方法可以避免网格重构、网格畸变等。基于Euler体系下的气动声学波动方程，推导了Lagrange体系下声波传播的控制方程，并建立了无网格光滑粒子动力学（smoothed particle hydrodynamics，SPH）方法的数值离散格式。通过对比静止流体中声传播问题的SPH解和时域有限差分（finite difference time domain，FDTD）解，验证了SPH方法在声学计算中的准确性和可靠性。对于一维和二维流动流体中的声传播问题，通过与基于Doppler效应的理论解对比，阐明了利用SPH方法求解复杂气动声学问题的可行性。
Abstract
Simulation of human sound wave propagation need to take into account the moving boundaries and fluid flow within the vocal tract for accurate realistic models. Traditional mesh-based methods that are widely used to study human sound production have many problems due to mesh reconstruction and distortion, so they are not as effective as meshless methods. The aeroacoustic wave equations in the Eulerian framework are transformed to the governing equations for wave propagation in the Lagrangian form and discretized using the smoothed particle hydrodynamics (SPH) method. The accuracy and reliability of SPH for wave propagation in a static media are shown by comparisons with finite difference time domain (FDTD) results. This method is validated against the Doppler effect based theoretical solutions for one-and two-dimensional aeroacoustics to verify the ability of SPH to solve complex aeroacoustic problems.
关键词
气动声学 /
声道 /
无网格 /
光滑粒子动力学 /
Lagrange方法
Key words
aeroacoustics /
vocal tract /
meshless /
smoothed particle hydrodynamics /
Lagrangian method
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参考文献
[1] Stevens K N. Acoustic Phonetics[M]. Cambridge:The MIT Press, 2000. [2] CHEN Xi, DANG Jianwu, YAN Han, et al. A neural understanding of speech motor learning[C]//Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA 2013). Kaohsiung, Taiwan, China:IEEE Press, 2013:321-325. [3] Lighthill M J. On sound generated aerodynamically:II. Turbulence as a source of sound[J]. Proc R Soc Lond A, 1954, 222:1-32. [4] Tam C K W. Computational aeroacoustics:Issues and methods[J]. AIAA J, 1995, 33(10):1788-1796. [5] Tam C K W, Webb J C. Dispersion-relation-preserving finite difference scheme for computational acoustics[J]. J Comput Phys, 1993, 107(2):262-281. [6] Lele S K. Compact finite difference scheme with spectral-like resolution[J]. J Comput Phys, 1992, 103(1):16-42. [7] Kim J W, Lee D J. Optimized compact finite difference schemes with maximum resolution[J]. AIAA J, 1996, 34(5):887-893. [8] Zhong X L. High-order finite-difference schemes for numerical simulation of hypersonic boundary-layer transition[J]. J Comput Phys, 1998, 144(2):662-709. [9] Zhuang M, Chen R F. Optimized upwind dispersion relation preserving finite difference scheme for computational aeroacoustics[J]. AIAA J, 1998, 36(11):2146-2148. [10] Gaitonde D, Shang J S. Optimized compact difference based finite-volume schemes for linear wave phenomena[J]. J Comput Phys, 1997, 138(2):617-643. [11] Lee C, Seo Y. A new compact spectral scheme for turbulence simulation[J]. J Comput Phys, 2002, 183(2):438-469. [12] Hu F Q, Hussaini M Y, Manthey J L. Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics[J]. J Comput Phys, 1996, 124(1):177-191. [13] Cockburn B, Shu C W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II:general framework[J]. Math Comput, 1989, 52:411-435. [14] Liu G R, Liu M B. Smoothed Particle Hydrodynamics Methed:A Meshfree Pariticle Method[M]. Singapore:World Scientific Press, 2003. [15] 张德良. 计算流体力学教程[M]. 北京:高等教育出版社, 2010. ZHANG Deliang. A Course in Computational Fluid Dynamics[M]. Beijing:Higher Education Press, 2010. (in Chinese) [16] Lucy L B. A numerical approach to the testing of the fission hypothesis[J]. Astron J, 1977, 8(12):1013-1024. [17] Gingold R A, Monaghan J J. Smoothed particle hydrodynamics:Theory and applications to non-spherical stars[J]. MNRAS, 1977, 18:375-389. [18] Monaghan J J. Smoothed particle hydrodynamics and its diverse applications[J]. Ann Rev Fluid Mech, 2012, 44(44):323-346. [19] Lastiwka M, Basa M, Quinlan N J. Permeable and non-reflecting boundary conditions in SPH[J]. Int J Numer Methods Fluids, 2009, 61:709-724. [20] HOU Qingzhi, Kruisbrink A C H, Pearce F, et al. Smoothed particle hydrodynamics simulations of flow separation at bends[J]. Comput Fluids, 2014, 90(4):138-146. [21] Sullivan D M. Electromagnetic Simulation Using the FDTD Method[M]. New York:John Wiley & Sons, 2013.
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