TY - JOUR
T1 - A Novel Lattice Boltzmann Model for Fourth Order Nonlinear Partial Differential Equations
AU - Qiao, Zhonghua
AU - Yang, Xuguang
AU - Zhang, Yuze
N1 - Funding Information:
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.
Funding Information:
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.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/5
Y1 - 2021/5
N2 - 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.
AB - 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.
KW - Cahn–Hilliard equation
KW - Fourth order nonlinear partial differential equation
KW - Lattice Boltzmann method
UR - https://www.scopus.com/pages/publications/85103828048
U2 - 10.1007/s10915-021-01471-6
DO - 10.1007/s10915-021-01471-6
M3 - Journal article
AN - SCOPUS:85103828048
SN - 0885-7474
VL - 87
SP - 1
EP - 18
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
M1 - 51
ER -