Simulation of the Nonlinear Heat Conduction Equation With the Lattice Boltzmann Method

LIU Fang; SHI Wei-ping

doi:10.3879/j.issn.1000-0887.2015.11.004

Volume 36 Issue 11

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LIU Fang, SHI Wei-ping. Simulation of the Nonlinear Heat Conduction Equation With the Lattice Boltzmann Method[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1158-1166. doi: 10.3879/j.issn.1000-0887.2015.11.004

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Simulation of the Nonlinear Heat Conduction Equation With the Lattice Boltzmann Method

doi: 10.3879/j.issn.1000-0887.2015.11.004

LIU Fang¹,
SHI Wei-ping²

¹School of Basic Sciences, Changchun University of Technology, Changchun 130012, P.R.China;²Mathematics School, Jilin University, Changchun 130012, P.R.China

Funds: The National Natural Science Foundation of China(11401046)

Received Date: 2015-07-10
Rev Recd Date: 2015-08-20
Publish Date: 2015-11-15

Abstract

Abstract

A lattice Boltzmann model for the heat conduction equation with a nonlinear source term and a nonlinear diffusion term was presented. 2 differential operators related to the source term distribution function were added to the evolution equation, on which the ChapmanEnskog expansion was carried out. Then, through some further improvement of the evolution equation the macroscopic differential equation was recovered in 2 schemes with highorder truncation errors. Detailed numerical simulations of the nonlinear heat conduction equation with different parameter selections were performed. The numerical results agree well with the exact solutions. This model can also be directly used to numerically solve other partial differential equations in similar forms.
- lattice Boltzmann model,
- nonlinear heat conduction equation,
- lattice BhatnagarGrossKrook model,
- nonlinear source term

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References(15)

References

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