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A Novel Lattice Boltzmann Model for Fourth Order Nonlinear Partial Differential Equations
Journal of Scientific Computing ( IF 2.5 ) Pub Date : 2021-04-02 , DOI: 10.1007/s10915-021-01471-6
Zhonghua Qiao , Xuguang Yang , Yuze Zhang

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.



中文翻译:

四阶非线性偏微分方程的一个新的Lattice Boltzmann模型。

为了解决四阶非线性偏微分方程(NPDE),提出了一种新型的格子玻尔兹曼方程(LB)方程模型。与现有的LB模型不同,引入了源分布函数以消除方程式非线性部分中的某些不需要的项。因此,平衡分布函数的设计遵循Chapman–Enskog(C–E)分析的规则。通过C–E程序,可以从建议的LB模型中完美地恢复四阶NPDE。为了解决一些广泛研究的四阶NPDE,已经进行了一系列数值实验,包括Kuramoto–Sivashinsky方程,具有双阱势的Cahn–Hilliard方程和具有Peng–Robinson状态方程的四阶扩散界面模型。

更新日期:2021-04-04
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