Aix Marseille Univ, CNRS, Centrale Marseille, M2P2 UMR 7340, 13451 Marseille, France.
National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.
Phys Rev E. 2017 Jun;95(6-1):063301. doi: 10.1103/PhysRevE.95.063301. Epub 2017 Jun 6.
In this paper, a variant of the acoustic multipole source (AMS) method is proposed within the framework of the lattice Boltzmann method. A quadrupole term is directly included in the stress system (equilibrium momentum flux), and the dependency of the quadrupole source in the inviscid limit upon the fortuitous discretization error reported in the works of E. M. Viggen [Phys. Rev. E 87, 023306 (2013)PLEEE81539-375510.1103/PhysRevE.87.023306] is removed. The regularized lattice Boltzmann (RLB) method with this variant AMS method is presented for the 2D and 3D acoustic problems in the inviscid limit, and without loss of generality, the D3Q19 model is considered in this work. To assess the accuracy and the advantage of the RLB scheme with this AMS for acoustic point sources, the numerical investigations and comparisons with the multiple-relaxation-time (MRT) models and the analytical solutions are performed on the 2D and 3D acoustic multipole point sources in the inviscid limit, including monopoles, x dipoles, and xx quadrupoles. From the present results, the good precision of this AMS method is validated, and the RLB scheme exhibits some superconvergence properties for the monopole sources compared with the MRT models, and both the RLB and MRT models have the same accuracy for the simulations of acoustic dipole and quadrupole sources. To further validate the capability of the RLB scheme with AMS, another basic acoustic problem, the acoustic scattering from a solid cylinder presented at the Second Computational Aeroacoustics Workshop on Benchmark Problems, is numerically considered. The directivity pattern of the acoustic field is computed at r=7.5; the present results agree well with the exact solutions. Also, the effects of slip and no-slip wall treatments within the regularized boundary condition on this pure acoustic scattering problem are tested, and compared with the exact solution, the slip wall treatment can present a better result. All simulations demonstrate that the RLB scheme with the AMS method is capable of accurately simulating 2D and 3D acoustic generation, propagation, and scattering at zero viscosity.
本文在格子玻尔兹曼方法的框架内提出了声学多极声源（AMS）方法的一个变体。四极项直接包含在应力系统（平衡动量通量）中，并且在无粘极限下，四极源对 Viggen [Phys. Rev. E 87, 023306 (2013) PLEEE81539-375510.1103/PhysRevE.87.023306] 工作中报道的偶然离散误差的依赖性被消除。提出了带有此变体 AMS 方法的正则化格子玻尔兹曼（RLB）方法，用于无粘极限下的 2D 和 3D 声学问题，并且在这项工作中，无损失地考虑了 D3Q19 模型。为了评估 RLB 方案带有此 AMS 方法的准确性和优势，用于声学点源，在无粘极限下对 2D 和 3D 声学多极点源进行了数值研究和与多松弛时间（MRT）模型和解析解的比较，包括单极子、x 偶极子和 xx 四极子。从目前的结果来看，验证了此 AMS 方法的高精度，并且与 MRT 模型相比，RLB 方案对单极子源表现出一些超收敛特性，并且 RLB 和 MRT 模型对声学偶极子和四极子源的模拟具有相同的精度。为了进一步验证带有 AMS 的 RLB 方案的能力，还考虑了另一个基本声学问题，即第二届计算气动声学基准问题研讨会上提出的固体圆柱体的声学散射问题。在 r=7.5 处计算了声场的指向性图；目前的结果与精确解吻合良好。此外，还测试了正则化边界条件中滑移和无滑移壁处理对这个纯声学散射问题的影响，并与精确解进行了比较，滑移壁处理可以得到更好的结果。所有的模拟都表明，带有 AMS 方法的 RLB 方案能够准确地模拟零粘度下的 2D 和 3D 声学产生、传播和散射。
