A Novel Lattice Boltzmann Model for Fourth Order Nonlinear Partial Differential Equations

Zhonghua Qiao, Xuguang Yang, Yuze Zhang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.
Original languageEnglish (US)
JournalJournal of Scientific Computing
Issue number2
StatePublished - Apr 2 2021
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-07-01
Acknowledgements: The authors are grateful to the referees for careful reading and constructive comments that improved the quality of this paper. The authors also appreciate the valuable discussions with Prof. Shuyu Sun in King Abdullah University of Science and Technology. Z. Qiao’s work is partially supported by Hong Kong Research Council GRF Grant 15325816 and the Hong Kong Polytechnic University internal research fund G-UAEY. X. Yang’s work is partially supported by the Natural Science Foundation of China (Grant No. 11802090) and the Hong Kong Polytechnic University Postdoctoral Fellowships Scheme 1-YW1D.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Software
  • General Engineering


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