Lattice boltzmann model for nonlinear heat equations

Authors:
Qiaojie Li;Zhoushun Zheng;Shuang Wang;Jiankang Liu
Affiliations:
School of Mathematics and Statistics, Central South University, Changsha, P.R. China;School of Mathematics and Statistics, Central South University, Changsha, P.R. China;School of Mathematics and Statistics, Central South University, Changsha, P.R. China;School of Mathematics and Statistics, Central South University, Changsha, P.R. China
Venue:
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
Year:
2012

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Abstract

In this paper, a lattice Boltzmann scheme with an amending function for the nonlinear heat equations with the form ∂tφ=α∇2φ+ψ(φ) which directly to solve some important nonlinear equations, including Fisher equation, Newell-Whitehead equation and FitzHugh-Nagumo equation is proposed . Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions or the numerical solutions reported in previous studies.