Solution of Non-linear PDEs

Lattice Boltzmann Method LBM: Theory
#1

Big Hi for you all
I,m new in this useful forum. I search the topics but I can’t find anything about solving non-linear partial differential equation with 1-D lattice Boltzmann models (D1Q5,D1Q7).
Is there anybody who has experience in simulating and recovering evolution equations such as Burgers equation, KdV equation, …
I have some problems in my FORTRAN code about the above topic so I really appriciate if you can help me.

One of my ref. paper: A unified lattice Boltzmann model for some nonlinear partial differential equations, Zhenhua Chaia, Baochang Shib
and Lin Zhengb, ScienceDirect, Chaos, Solutions and Fractals 36 (2008), 874-882

Best Regards

#2

Thanks you for the post.
Hi guys, Im a newbie. Nice to join this forum.

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#3

Dear Minorswing,

I am a newbie too, and have no experience about that, but I have read some articles about that:
Lattice Boltzmann method for one and two-dimensional Burgers equation,Jianying Zhang, Guangwu Yan,Physica A 387 (2008) 4771–4786
A higher-order moment method of the lattice Boltzmann model for the Korteweg–de Vries equation,G. Yan, J. Zhang / Mathematics and Computers in Simulation 79 (2009) 1554–1565

Hope it will help,

shelley