Viscous absorbing boundary of the multiple-relaxation-time lattice Boltzmann method
JIANG Chuntao1,2, ZHOU Hui1,2, XIA Muming3,4,5, TANG Jinxuan1,2, WANG Ying6,7
1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum(Beijing), Beijing 102249, China; 2. CNPC Key Laboratory of Geophysical Exploration, China University of Petroleum(Beijing), Beijing 102249, China; 3. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China; 4. Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China; 5. Key Laboratory of Petroleum Resources Research, Chinese Academy of Sciences, Beijing 100029, China; 6. Beijing Institute of Aerospace Control Devices, Beijing 100094, China; 7. Beijing Engineering Research Center of Optical Fiber Sensing System, Beijing 100094, China
Abstract：When the geometric structure of the medium is complicated or there are strong physical discontinuities inside, the calculation results by traditional forward simulation methods of seismic waves are often difficult to meet the requirements of actual fine calculation for the wave field. The multiple-relaxation-time lattice Boltzmann method (MRT-LBM) is an emerging approach for numerical simulation, with good stability, high calculation accuracy, and flexible boundary processing. Aiming at the artificial truncated boundary faced by MRT-LBM numerical simulation, a viscous absorbing boundary scheme based on multiple relaxation parameters was proposed. Since the suppression effect of the boundary reflection was very sensitive to the attenuation parameters, massive numerical simulation experiments were conducted to determine the optimal parameter combination, and the absorbing boundary conditions with strong applicability were obtained. The absorbing boundary conditions were of a simple algorithm, with strong scalability. Finally, a uniform model and a simple heterogeneous model were built to verify the absorption effect, and a complex BP model was used to verify the applicability.
撒利明, 杨午阳, 姚逢昌, 等. 地震反演技术回顾与展望[J]. 石油地球物理勘探, 2015, 50(1):184-202.SA Liming, YANG Wuyang, YAO Fengchang, et al. Review and prospect of seismic inversion technology[J]. Oil Geophysical Prospecting, 2015, 50(1):184-202.
[2]
刘张聚, 童思友, 方云峰, 等. 基于时域加权的拉普拉斯-频率域弹性波全波形反演[J]. 石油地球物理勘探, 2021, 56(2):302-312.LIU Zhangju, TONG Siyou, FANG Yunfeng, et al. Full elastic waveform inversion in Laplace-Fourier domain based on time domain weighting[J]. Oil Geophysical Prospecting, 2021, 56(2):302-312.
[3]
王华忠. "两宽一高"油气地震勘探中的关键问题分析[J]. 石油物探, 2019, 58(3):313-324.WANG Huazhong. Key problem analysis in seismic exploration based on wide-azimuth, high-density, and broadband seismic data[J]. Geophysical Prospecting for Petroleum, 2019, 58(3):313-324.
[4]
陈汉明, 汪燚林, 周辉. 一阶速度-压力常分数阶黏滞声波方程及其数值模拟[J]. 石油地球物理勘探, 2020, 55(2):302-310.CHEN Hanming, WANG Yilin, ZHOU Hui. A novel constant fractional-order Laplacians viscoacoustic wave equation and its numerical simulation method[J]. Oil Geophysical Prospecting, 2020, 55(2):302-310.
[5]
Krüger T, Kusumaatmaja H, Kuzmin A, et al. The lattice Boltzmann method[J]. Springer International Publishing, 2017, 10(978-3):4-15.
[6]
Xu H, Sagaut P. Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics[J]. Journal of Computational Physics, 2011, 230(13):5353-5382.
[7]
He X, Doolen G D. Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows[J]. Journal of Statistical Physics, 2002, 107(1-2):309-328.
[8]
Xia M, Wang S, Zhou H, et al. Modelling viscoacoustic wave propagation with the lattice Boltzmann me-thod[J]. Scientific Reports, 2017, 7(1):1-9.
[9]
McNamara G R, Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata[J]. Physical Review Letters, 1988, 61(20):2332.
李幼铭, 胡健行. 细胞自动机在地震波传播研究中的应用[J]. 地球物理学报, 1995, 38(5):651-661.LI Youming, HU Jianxing. Application of cellular automata approach to the study of seismic wave propagation[J]. Chinese Journal of Geophysics, 1995, 38(5):651-661.
[12]
刘舒考, 刘雯林. 格子气自动机模型——一种地震数据正演研究的新方法[J]. 石油地球物理勘探, 1998, 33(5):658-662.LIU Shukao, LIU Wenlin. Lattice gas automata mo-del:A new method for seismic data forward simulation[J]. Oil Geophysical Prospecting, 1998, 33(5):658-662.
[13]
王真理, 李幼铭. 细胞自动机地震波模拟的并行化算法[J]. 地球物理学报, 1999, 42(3):410-415.WANG Zhenli, LI Youming. Parallel algorithm for simulating seismic wave propagation by cellular automata[J]. Chinese Journal of Geophysics, 1999, 42(3):410-415.
[14]
刘劲松, 许云, 刘福田, 等. 细胞自动机用于地震偏移:数值模拟试验[J]. 地球物理学进展, 2004, 19(3):621-624.LIU Jinsong, XU Yun, LIU Futian, et al. Numerical experiment of seismic migration using cellular auto-mata[J]. Progress in Geophysics, 2004, 19(3):621-624.
[15]
贺艳晓. 基于细胞自动机方法的地震波场模拟研究[D]. 北京:中国石油大学(北京), 2011.
[16]
Jiang C, Zhou H, Xia M, et al. Stability analysis of multiple-relaxation-time lattice Boltzmann model for wave simulation[C]. SEG Technical Program Expanded Abstracts, 2020, 39:2699-2703.
Berenger J P. A perfectly matched layer for the absorption of electromagnetic waves[J]. Journal of Computational Physics, 1994, 114(2):185-200.
[19]
Vergnault E, Malaspinas O, Sagaut P. A lattice Boltzmann method for nonlinear disturbances around an arbitrary base flow[J]. Journal of Computational Phy-sics, 2012, 231(24):8070-8082.
[20]
Najafi-Yazdi A, Mongeau L. An absorbing boundary condition for the lattice Boltzmann method based on the perfectly matched layer[J]. Computers & Fluids, 2012, 68:203-218.
Jiang C, Zhou H, Xia M, et al. Study on absorbing boundary conditions of viscous sponge layers based on lattice Boltzmann method[C]. Extended Abstracts of 82nd EAGE Conference & Exhibition, 2020, 1-5.
[23]
陈可洋. 完全匹配层吸收边界条件研究[J]. 石油物探, 2010, 49(5):472-477.CHEN Keyang. Study on perfectly matched layer absorbing boundary condition[J]. Geophysical Prospecting for Petroleum, 2010, 49(5):472-477.
