间断伽辽金玻尔兹曼方法中的基于完全耦合层技术的吸收边界条件研究
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摘要
本文发展了一种基于完全耦合层技术的吸收边界条件,并将其融合到具有低耗散和低色散性质的格子玻尔兹曼方法中。通过坐标变换保证了吸收边界条件的无条件稳定,通过解耦时间积分方法实现了交点间断伽辽金有限元方法求解对流过程。采用二维高斯脉动波和等温涡对迁移两个算例研究了完全耦合层厚度、指数分布因子和最大衰减系数对边界无反射能力的影响,采用双腔流噪声算例研究了吸收边界条件的长时间稳定性和非均匀伪平均流的有效性。结果表明本文发展的吸收边界条件表现良好,并可将其进一步发展到实际气动噪声计算问题中。
An absorbing boundary condition based on the perfectly matched layer technique is developed. It is combined with lattice Boltzmann method, which has low dissipative and low dispersive properties. By means of the coordinate transformation, unconditional stability is ensured. Invoking the decoupling time integration, we can solve the streaming process with nodal discontinuous Galerkin method. Two-dimensional Gauss waves and isothermal vortex migration are used to study the effect of layer thickness, index and maximum decaying coefficient on the non-reflecting performance. Double cavity flow noise is used to study the long time stability and the inhomogeneous pseudo mean flow.The result shows good performance, indicating the application of the absorbing boundary condition to real-life computational aeroacoustics.
An absorbing boundary condition based on the perfectly matched layer technique is developed. It is combined with lattice Boltzmann method, which has low dissipative and low dispersive properties. By means of the coordinate transformation, unconditional stability is ensured. Invoking the decoupling time integration, we can solve the streaming process with nodal discontinuous Galerkin method. Two-dimensional Gauss waves and isothermal vortex migration are used to study the effect of layer thickness, index and maximum decaying coefficient on the non-reflecting performance. Double cavity flow noise is used to study the long time stability and the inhomogeneous pseudo mean flow.The result shows good performance, indicating the application of the absorbing boundary condition to real-life computational aeroacoustics.
引文
[1] Marie S, Ricot D, Sagaut P. Comparison Between Lattice Boltzmann Method and Navier-Stokes High Order Schemes for Computational Aeroacoustics[J]. Journal of Computational Physics, 2009, 228:1056-1070
[2] Izquierdo S, Fueyo N. Characteristic Nonreflecting Boundary Conditions for Open Boundaries in Lattice Boltzmann Methods[J]. Physical Review E, 2008, 78:6707-6713
[3] Najafi-yazdi A, Mongeau L. An Absorbing Boundary Condition for the Lattice Boltzmann Method Based on the Perfectly Matched Layer[J]. Computer&Fluids, 2012,68:203-218
[4] Qian Y H, D'Humières D, Lallemand P. Lattice BGK Models for Navier-Stokes Equation[J]. Europhys Lett,1992, 17:479-484
[5] 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, 227:4398-4424
[6] Becache E, Fauqueux S, Joly P. Stability of Perfectly Matched Layers, Group Velocities and Anisotropic Waves[J]. Journal of Computational Physics, 2003, 188:399-433
[7] Lee T, Lin C L. An Eulerian Description of the Streaming Process in the Lattice Boltzmann Equation[J]. Journal of Computational Physics, 2003, 185:445-471
[8] Spiteri R J, Ruuth S J. A new Class of Optimal High-order Strong-Stability-Preserving time Discretization Methods[J]. SIAM Journal on Numerical Analysis, 2002, 40:469-491
[9]邵卫东,李军.计算气动声学中的伽辽金玻尔兹曼方法研究[J].西安交通大学学报,2016, 50:134-140Shao W D, Li J. Study on the Galerkin Boltzmann method for computational aeroacoustics[J]. Journal of Xi'an Jiaotong University, 2016, 50:134-140
[10]邵卫东,李军.格子玻尔兹曼方法中的特征无反射边界条件研究[J].工程热物理学报,2018, 39(2):277-285Shao W D, Li J. Characteristic Boundary Condition in Lattice Boltzmann Method[J]. Journal of Engineering Thermophysics, 2018, 39(2):277-285
[11] Shao W D, Li J. Analytical and Numerical Investigations on the Aeroacoustical Oscillation of Flow past the Cavity[C]//ASME Turbo Expo 2015, Montreal:Canada, Paper No.GT2015-42551
[12] Shao W D, Li J. Subsonic Flow Over Open Cavities:Part 1 Analytical Models and Numerical Investigations[C]//ASME Turbo Expo 2016, Seoul:South Korea, Paper No.GT2016-56414
[13] Shao W D, Li J. Subsonic Flow Over Open Cavities:Part2 Passive Control Methods[C]//ASME Turbo Expo 2016,Seoul:South Korea, Paper No.GT2016-56415
[2] Izquierdo S, Fueyo N. Characteristic Nonreflecting Boundary Conditions for Open Boundaries in Lattice Boltzmann Methods[J]. Physical Review E, 2008, 78:6707-6713
[3] Najafi-yazdi A, Mongeau L. An Absorbing Boundary Condition for the Lattice Boltzmann Method Based on the Perfectly Matched Layer[J]. Computer&Fluids, 2012,68:203-218
[4] Qian Y H, D'Humières D, Lallemand P. Lattice BGK Models for Navier-Stokes Equation[J]. Europhys Lett,1992, 17:479-484
[5] 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, 227:4398-4424
[6] Becache E, Fauqueux S, Joly P. Stability of Perfectly Matched Layers, Group Velocities and Anisotropic Waves[J]. Journal of Computational Physics, 2003, 188:399-433
[7] Lee T, Lin C L. An Eulerian Description of the Streaming Process in the Lattice Boltzmann Equation[J]. Journal of Computational Physics, 2003, 185:445-471
[8] Spiteri R J, Ruuth S J. A new Class of Optimal High-order Strong-Stability-Preserving time Discretization Methods[J]. SIAM Journal on Numerical Analysis, 2002, 40:469-491
[9]邵卫东,李军.计算气动声学中的伽辽金玻尔兹曼方法研究[J].西安交通大学学报,2016, 50:134-140Shao W D, Li J. Study on the Galerkin Boltzmann method for computational aeroacoustics[J]. Journal of Xi'an Jiaotong University, 2016, 50:134-140
[10]邵卫东,李军.格子玻尔兹曼方法中的特征无反射边界条件研究[J].工程热物理学报,2018, 39(2):277-285Shao W D, Li J. Characteristic Boundary Condition in Lattice Boltzmann Method[J]. Journal of Engineering Thermophysics, 2018, 39(2):277-285
[11] Shao W D, Li J. Analytical and Numerical Investigations on the Aeroacoustical Oscillation of Flow past the Cavity[C]//ASME Turbo Expo 2015, Montreal:Canada, Paper No.GT2015-42551
[12] Shao W D, Li J. Subsonic Flow Over Open Cavities:Part 1 Analytical Models and Numerical Investigations[C]//ASME Turbo Expo 2016, Seoul:South Korea, Paper No.GT2016-56414
[13] Shao W D, Li J. Subsonic Flow Over Open Cavities:Part2 Passive Control Methods[C]//ASME Turbo Expo 2016,Seoul:South Korea, Paper No.GT2016-56415
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