NLS-Boussinesq方程的格子Boltzmann模型求解

doi:10.13438/j.cnki.jdzk.2025.02.001

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (2): 1-9.DOI: 10.13438/j.cnki.jdzk.2025.02.001

• 数学 • 下一篇

NLS-Boussinesq方程的格子Boltzmann模型求解

董亚茹,戴厚平,王晶

(吉首大学数学与统计学院,湖南吉首 416000)

出版日期:2025-03-25 发布日期:2025-04-30
作者简介:董亚茹(1998—),女,山东德州人,吉首大学数学与统计学院硕士研究生,主要从事微分方程数值解研究
基金资助:
湖南省教育厅科学研究重点项目(21A0329);湖南省自然科学基金资助项目(2021JJ30548)

Lattice Boltzmann Method for the NLS-Boussinesq Equation

DONG Yaru,DAI Houping,WANG Jing

(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2025-03-25 Published:2025-04-30

摘要/Abstract

摘要：对构建的双分布函数的一维、二维格子Boltzmann模型中的演化方程进行Taylor展开,再结合Chapman-Enskog多尺度展开技术,推导出平衡态分布函数和修正函数，进而恢复出非线性耦合的NLS-Boussinesq方程.

关键词： NLS-Boussinesq方程, 格子Boltzmann模型, Taylor展开, Chapman-Enskog多尺度展开

Abstract: A lattice Boltzmann model with dual distribution functions is developed,and the evolution equations in the model are Taylor expanded.The Chapman-Enskog multiscale expansion technique is combined to derive the equilibrium distribution functions and correction functions and then to recover the nonlinear coupled NLS-Boussinesq equations

Key words: NLS-Boussinesq equations, lattice Boltzmann method, Taylor expansion, Chapman-Enskog multiscale expansion

董亚茹, 戴厚平, 王晶. NLS-Boussinesq方程的格子Boltzmann模型求解[J]. 吉首大学学报（自然科学版）, 2025, 46(2): 1-9.

DONG Yaru, DAI Houping, WANG Jing. Lattice Boltzmann Method for the NLS-Boussinesq Equation[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(2): 1-9.

参考文献

[1] MILLS KYLE,SPANNER MICHAEL,TAMBLYN ISAAC.Deep Learning and the Schrdinger Equation[J].Physical Review A,2017,96(4):42-113.
[2] MADSEN P A,BINGHAM H B,SCHFFER H A.Boussinesq-Type Formulations for Fully Nonlinear and Extremely Dispersive Water Waves:Derivation and Analysis[J].Proceedings of the Royal Society of London.Series A:Mathematical,Physical and Engineering Sciences,2003,459(2033):1075-1104.
[3] LU Junliang,HONG Xiaochun,ZHAO Qi.New Exact Solutions for Coupled Schrdinger Boussinesq Equations[J].Journal of Applied Analysis and Computation,2021,11(2):741-765.
[4] HU Xiuling,WANG Shanshan,ZHANG Luming.Maximum Error Estimates for a Compact Difference Scheme of the Coupled Nonlinear Schrdinger-Boussinesq Equations[J].Numerical Methods for Partial Differential Equations,2019,35(6):1971-1999.
[5] ISMAIL M S,ASGI H A.A Compact Finite Difference Schemes for Solving the Coupled Nonlinear Schrodinger-Boussinesq Equations[J].Applied Mathematics,2016,7(7):605-615.
[6] LI Meng.Cut-Off Error Splitting Technique for Conservative Nonconforming VEM for N-Coupled Nonlinear Schrdinger-Boussinesq Equations[J].Journal of Scientific Computing,2022,93(3):86-91.
[7] DENG Dingwen,WU Qiang.Analysis of the Linearly Energy-and Mass-Preserving Finite Difference Methods for the Coupled Schrdinger-Boussinesq Equations[J].Applied Numerical Mathematics,2021,170:14-38.
[8] DENG Dingwen,WU Qiang.Linearized and Decoupled Structure-Preserving Finite Difference Methods and Their Analyses for the Coupled Schrdinger-Boussinesq Equations[J].Numerical Methods for Partial Differential Equations,2021,37(5):2924-2951.
[9] LIAO Feng,ZHANG Luming,WANG Tingchun.Unconditional L∞ Convergence of a Conservative Compact Finite Difference Scheme for the N-Coupled Schrdinger-Boussinesq Equations[J].Applied Numerical Mathematics,2019,138:54-77.
[10] LIAO Feng,ZHANG Luming,WANG Tingchun.Two Energy-Conserving and Compact Finite Difference Schemes for Two-Dimensional Schrdinger-Boussinesq Equations[J].Numerical Algorithms,2020,85:1335-1363.
[11] BAI Dongmei,ZHANG Luming.The Quadratic B-Spline Finite-Element Method for the Coupled Schrdinger-Boussinesq Equations[J].International Journal of Computer Mathematics,2011,88(8):1714-1729.
[12] BAI Dongmei,WANG Jianli.The Time-Splitting Fourier Spectral Method for the Coupled Schrdinger-Boussinesq Equations[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(3):1201-1210.
[13] LIAO Feng,ZHANG Luming,WANG Shanshan.Time-Splitting Combined with Exponential Wave Integrator Fourier Pseudospectral Method for Schrdinger-Boussinesq System[J].Communications in Nonlinear Science and Numerical Simulation,2018,55:93-104.
[14] 何雅玲,王勇,李庆.格子 Boltzmann 方法的理论及应用[M].北京:科学出版社,2009:2638-2656.
[15] YU Dazhi,MEI Renwei,LUO Lishi.Viscous Flow Computations with the Method of Lattice Boltzmann Equation[J].Progress in Aerospace Sciences,2003,39(5):329-367.
[16] 冯颖欣,戴厚平,汪辰,等.扩展Fisher-Kolmogorov方程的格子Boltzmann方法[J].吉首大学学报(自然科学版),2023,44(4):19-30.
[17] ZHANG Jianying,YAN Guangwu.Lattice Boltzmann Method for One and Two-Dimensional Burgers Equation[J].Physica A:Statistical Mechanics and Its Applications,2008,387(19/20):4771-4786.

NLS-Boussinesq方程的格子Boltzmann模型求解

Lattice Boltzmann Method for the NLS-Boussinesq Equation

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