Finite-difference lattice Boltzmann model for nonlinear convection-diffusion equations

2017 ◽  
Vol 309 ◽  
pp. 334-349 ◽  
Author(s):  
Huili Wang ◽  
Baochang Shi ◽  
Hong Liang ◽  
Zhenhua Chai
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Diffusion Equations ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Boltzmann Model

scholarly journals Rectangular lattice Boltzmann model for nonlinear convection–diffusion equations

2011 ◽  
Vol 369 (1944) ◽  
pp. 2311-2319 ◽  
Author(s):  
Jianhua Lu ◽  
Zhenhua Chai ◽  
Baochang Shi ◽  
Zhaoli Guo ◽  
Guoxiang Hou
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann ◽  
Equilibrium Distribution ◽  
Lattice Boltzmann Model ◽  
Diffusion Equations ◽  
Equilibrium Distribution Function ◽  
Rectangular Lattice ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Boltzmann Model

In this paper, a rectangular lattice Boltzmann model is proposed for nonlinear convection–diffusion equations (NCDEs). The model can be used to solve NCDEs with very general form by using a real/complex-valued quadric equilibrium distribution function and relaxation time. Detailed simulations on several examples are performed to validate the model. The numerical results show good agreement with the analytical solutions, and the numerical accuracy is much better than that of the models with a linear equilibrium distribution function.

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