A Novel Lattice Boltzmann Model for Fourth Order Nonlinear Partial Differential Equations
A Novel Lattice Boltzmann Model for Fourth Order Nonlinear Partial Differential Equations
复制标题
四阶非线性偏微分方程的新型格子玻尔兹曼模型
DOI：
10.1007/s10915-021-01471-6
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发表时间：
2021-05-01
影响因子：
2.5
通讯作者：
Zhang, Yuze
中科院分区：
文献类型：
--
作者：
Qiao, Zhonghua;Yang, Xuguang;Zhang, Yuze
In this paper, a novel lattice Boltzmann (LB) equation model is proposed to solve the fourth order nonlinear partial differential equation (NPDE). Different from existing LB models, a source distribution function is introduced to remove some unwanted terms in the nonlinear part of the equation. Hereby, the equilibrium distribution function is designed to follow the rule of Chapman-Enskog (C-E) analysis. Through the C-E procedure, the fourth order NPDE can be recovered perfectly from the proposed LB model. A series of numerical experiments have been carried out to solve some widely studied fourth order NPDEs, including the Kuramoto-Sivashinsky equation, Cahn-Hilliard equation with double-well potential and a fourth order diffuse interface model with Peng-Robinson equation of state. Numerical results show that the performance of the present LB model is much better than other existing LB models.
