一种适用计算声学问题的网格间断人工黏性分布策略
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摘要
在计算声学数值模拟过程中,当空间离散采用高阶有限差分格式时,在网格间断处易出现短波发散问题,易污染整个计算域的数值解。针对该问题,在对称模板DRP格式的基础上,探索了曲线坐标系下交界面、奇异点等间断处人工黏性添加策略;经过初始扰动绕圆柱传播算例的计算对比分析表明:声波随着时间推移,向空间逐步散开;当声波到达圆柱时,声波会发生部分反射现象,形成二次声源向空间传播,整个计算过程中未出现计算发散现象。研究结果表明,提出的人工黏性分布策略能有效解决间断处短波发散问题,为复杂构型的声场模拟提供技术支撑。
In computational acoustic numerical simulation processes, when a high-order finite difference scheme is used to do spatial discretization, short wave divergence problems are easy to occur at places of grid discontinuity to contaminate numerical solutions in the whole computational domain. Here, aiming at this problem, based on the symmetric template DRP scheme, the artificial viscous distribution strategy was explored at discontinuous places of interface surface and singular points, etc., under a curvilinear coordinate system. Through contrastively calculating an initial acoustic disturbance propagating around a cylinder, the analysis results showed that sound wave gradually disperses in space over time; when sound wave reaches a cylinder, sound wave partially reflects to form a secondary sound source to spread sound wave into space again; computation divergence phenomena don't happen in the whole computation process; so the proposed artificial viscous distribution strategy can effectively solve short wave divergence problems at discontinuous places, and provide a technical support for sound field simulations with complex configuration.
In computational acoustic numerical simulation processes, when a high-order finite difference scheme is used to do spatial discretization, short wave divergence problems are easy to occur at places of grid discontinuity to contaminate numerical solutions in the whole computational domain. Here, aiming at this problem, based on the symmetric template DRP scheme, the artificial viscous distribution strategy was explored at discontinuous places of interface surface and singular points, etc., under a curvilinear coordinate system. Through contrastively calculating an initial acoustic disturbance propagating around a cylinder, the analysis results showed that sound wave gradually disperses in space over time; when sound wave reaches a cylinder, sound wave partially reflects to form a secondary sound source to spread sound wave into space again; computation divergence phenomena don't happen in the whole computation process; so the proposed artificial viscous distribution strategy can effectively solve short wave divergence problems at discontinuous places, and provide a technical support for sound field simulations with complex configuration.
引文
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[12] 吴继飞,罗新福,范召林.内埋式弹舱流场特性及武器分离特性改进措施[J].航空学报,2009,30(10):23-31.WU Jifei,LUO Xinfu,FAN Zhaolin.Flow control method to improve cavity flow and store separation characteristics[J].Acta Aeronautica et Astronautica Sinica,2009,30(10):23-31.
[2] BERGER M,JAMESON A.Automatic adaptive grid refinement for the euler equations[J].AIAA Journal,1985,23(1):561-572.
[3] TAM C K W,WEBB J C.A study of the short wave components in computational acoustics[J].Journal of Computational Acoustics,1993,1(1):1-30.
[4] ENGQUIST B.Nonlinear filters for efficient shock computation[J].Mathematics of Computation,1989,52(2):509-537.
[5] 王泽晖,罗柏华,刘宇陆.在计算气动声学中用非线性滤波法消除短波[J].上海大学学报(自然科学版),2004,10(4):393-399.WANG Zehui,LUO Baihua,LIU Yulu.Elimination of short waves in computational aeroacoustics using a nolinear filter[J].Jouranl of Shanghai University (Natural Science),2004,10(4):393-399.
[6] TAM C K W,KURBATSKII K A.Multi-size-mesh multi-time-step dispersion-relation-preserving scheme for multiple-scales aeroacoustics problems[J].International Journal of Computational Fluid Dynamics,2005,17(2):119-132.
[7] HU F Q.On constructing stable perfectly matched layers as an absorbing boundary condition for Euler equations[C].AIAA-2002-0227.
[8] HU F Q.A stable,perfectly matched layer for linearized Euler equations in un-split physical variables[J].Journal of Computational Physical,2001,173(2):455-480.
[9] HU F Q,LI X D,LIN D K.Absorbing boundary conditions for nonlinear Euler and Navier-Stokes equations based on the perfectly matched layer technique[J].Journal of Computational Physics,2008,227(1):4398-4424.
[10] TAM C K W.Compational aeroacoustics:a wave number approach[M].Comtridge:Cambridge University Press,2015.
[11] TAM C K W,HARDIN J C.Second computational aeroacoustics (CAA) workshop on benchmark problems[C]∥NASA Conference Publication 3352,1997.
[12] 吴继飞,罗新福,范召林.内埋式弹舱流场特性及武器分离特性改进措施[J].航空学报,2009,30(10):23-31.WU Jifei,LUO Xinfu,FAN Zhaolin.Flow control method to improve cavity flow and store separation characteristics[J].Acta Aeronautica et Astronautica Sinica,2009,30(10):23-31.