扩展Fisher-Kolmogorov方程的格子Boltzmann方法

doi:10.13438/j.cnki.jdzk.2023.04.003

吉首大学学报（自然科学版） ›› 2023, Vol. 44 ›› Issue (4): 19-30.DOI: 10.13438/j.cnki.jdzk.2023.04.003

扩展Fisher-Kolmogorov方程的格子Boltzmann方法

冯颖欣，戴厚平，汪辰，魏雪丹

(吉首大学数学与统计学院，湖南吉首 416000)

出版日期:2023-07-25 发布日期:2023-07-26
通讯作者: 戴厚平(1979—),男,湖南邵阳人,吉首大学数学与统计学院副教授,博士,主要从事微分方程数值解研究.
作者简介:冯颖欣(1998—),女,陕西铜川人,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:
湖南省自然科学基金资助项目(2021JJ30548);湖南省教育厅科学研究重点项目(21A0329);吉首大学校级科研项目(JDY22006);湖南省教育厅科学研究一般项目(22C0279)

Lattice Boltzmann Numerical Method for the Extended Fisher-Kolmogorov Equation

FENG Yingxin,DAI Houping,WANG Chen,WEI Xuedan

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

Online:2023-07-25 Published:2023-07-26

摘要/Abstract

摘要：基于格子Boltzmann方法构造了一种新的求解扩展Fisher-Kolmogorov(EFK)方程的数值格式.利用Taylor展开和Chapman-Enskog多尺度展开技术,得到一维、二维EFK方程格子Boltzmann模型的局部平衡态分布函数和修正函数,进一步恢复对应宏观方程.在此基础上,推导出模型迭代格式的稳定性条件,并利用模型求解EFK方程的初边值问题.

关键词： 扩展Fisher-Kolmogorov方程, 格子Boltzmann方法, 数值计算, 稳定性

Abstract: A new numerical format for solving the extended Fisher-Kolmogorov (EFK) equation is constructed based on the lattice Boltzmann method.The Taylor expansion and Chapman-Enskog multiscale expansion techniques are used to obtain the local equilibrium state distribution functions and correction functions of the lattice Boltzmann model for the one-and two-dimensional EFK equations,and to further recover the corresponding macroscopic equations.On this basis,stability conditions for the iterative format of the model are derived,and the model is used to solve the initial marginal value problem of the EFK equation.

Key words: extended Fisher-Kolmogorov equation, lattice Boltzmann method, numerical computation, stability analysis

冯颖欣, 戴厚平, 汪辰, 魏雪丹. 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.

FENG Yingxin, DAI Houping, WANG Chen, WEI Xuedan. Lattice Boltzmann Numerical Method for the Extended Fisher-Kolmogorov Equation[J]. Journal of Jishou University(Natural Sciences Edition), 2023, 44(4): 19-30.

参考文献

[1] COULLET P,ELPHICK C,REPAUX D.Nature of Spatial Chaos[J].Physical Review Letters,1987,58:431-434.
[2] DEE G T,VAN SAARLOOS WIM.Bistable Systems with Propagating Fronts Leading to Pattern Formation[J].Physical Review Letters,1988,60(25):2641-2644.
[3] ARONSON D G,WEINBERGER H F.Multidimensional Nonlinear Diffusion Arising in Population Genetics[J].Advances in Mathematics,1978,30(1):33-76.
[4] ZHU Guozhen.Experiments on Director Waves in Nematic Liquid Crystals[J].Physical Review Letters,1982,49(18):1332-1335.
[5] HORNREICH R M,LUBAN MARSHALL,SHTRIKMAN S.Critical Behavior at the Onset of k〖DD（-*2〗→〖DD）〗-Space Instability on the λ Line[J].Physical Review Letters,1975,35(25):1678-1681.
[6] 李娟,高广花.二维扩展Fisher-Kolmogorov方程的线性化紧差分格式的最大模误差分析[J].西南师范大学学报(自然科学版),2017,42(3):12-21.
[7] SWEILAMN H,ELSAKOUT D M,MUTTARDI M M.Numerical Solution for Stochastic Extended Fisher-Kolmogorov Equation[J].Chaos,Solitons and Fractals,2021,151:111213.DOI:10.1016/j.chaos.2021.111213.
[8] LI Shuguang,XU Da,ZHANG Jie,et al.A New Three-Level Fourth-Order Compact Finite Difference Scheme for the Extended Fisher-Kolmogorov Equation[J].Applied Numerical Mathematics,2022,178:41-51.
[9] DANUMJAYA P,PANI AMIYA K.Orthogonal Cubic Spline Collocation Method for the Extended Fisher-Kolmogorov Equation[J].Journal of Computational and Applied Mathematics,2005,174(1):101-117.
[10] MITTAL R C,DAHIYA SUMITA.A Study of Quintic B-Spline Based Differential Quadrature Method for a Class of Semi-Linear Fisher-Kolmogorov Equations[J].Alexandria Engineering Journal,2016,55(3):2893-2899.
[11] LI Xiang,DONG Zhiqiang,LI Yan,et al.A Fractional-Step Lattice Boltzmann Method for Multiphase Flows with Complex Interfacial Behavior and Large Density Contrast[J].International Journal of Multiphase Flow,2022,149:103982.DOI:10.1016/j.ijmultiphaseflow.2022.103982.
[12] SHAN Fang,DU Hongyan,CHAI Zhenhua,et al.Lattice Boltzmann Modeling of the Capillary Rise of Non-Newtonian Power-Law Fluids[J].International Journal for Numerical Methods in Fluids,2022,94(3):251-271.
[13] HAN Wenbo,CHEN Xueye.A Review on Microdroplet Generation in Microfluidics[J].Journal of the Brazilian Society of Mechanical Sciences and Engineering,2021,43(5):247.DOI:10.1007/s40430-021-02971-0.
[14] 戴厚平,郑洲顺,段丹丹.变系数反应扩散方程的格子Boltzmann模型[J].云南大学学报(自然科学版),2016,38(4):524-529.
[15] KATAOKA TAKESHI,HANADA TAKAYA.New Lattice Boltzmann Model for the Compressible Navier-Stokes Equations[J].International Journal for Numerical Methods in Fluids,2019,91(4):183-197.
[16] 魏雪丹,戴厚平,李梦军,等.一维空间Riesz分数阶对流扩散方程的格子Boltzmann方法[J].计算物理,2021,38(6):683-692.
[17] 张继红,栾舒含,梁波.具非线性对流项热传导方程的有限差分法[J].大连交通大学学报,2022,43(5):115-117.
[18] SHAH KAMAL,NAZ HAFSA,SARWAR MUHAMMAD,et al.On Spectral Numerical Method for Variable-Order Partial Differential Equations[J].AIMS Mathematics,2022,7(6):10422-10438.
[19] IBRAHEEM GHADA H,TURKYILMAZOGLU MUSTAFA,AL-JAWARY M A.Novel Approximate Solution for Fractional Differential Equations by the Optimal Variational Iteration Method[J].Journal of Computational Science,2022,64:101841.DOI:10.1016/j.jocs.2022.101841.
[20] DEHGHAN MEHDI,SHAFIEEABYANEH NASIM.Local Radial Basis Function-Finite-Difference Method to Simulate Some Models in the Nonlinear Wave Phenomena:Regularized Long-Wave and Extended Fisher-Kolmogorov Equations[J].Engineering with Computers,2021,37:1159-1179.

扩展Fisher-Kolmogorov方程的格子Boltzmann方法

Lattice Boltzmann Numerical Method for the Extended Fisher-Kolmogorov Equation

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