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Title: A novel lattice Boltzmann model for fourth order nonlinear partial differential equations
Authors: Qiao, Z 
Yang, X
Zhang, Y
Issue Date: May-2021
Source: Journal of scientific computing, May 2021, v. 87, no. 2, 51
Abstract: 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.
Keywords: Cahn–Hilliard equation
Fourth order nonlinear partial differential equation
Lattice Boltzmann method
Publisher: Springer
Journal: Journal of scientific computing 
ISSN: 0885-7474
DOI: 10.1007/s10915-021-01471-6
Rights: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at:
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