外力项在计算平衡态速度时加入一次，在计算宏观速度时又加入一次，为什么加入了两次？

huadie

外力项在计算平衡态速度时加入一次，在计算宏观速度时又加入一次，为什么加入了两次？
看截图。

luo@odu.edu

Why not contact the author(s) directly for an answer?

huadie

Dear Prof. Luo,

     Thank you very much for your suggestion! I will try in that way.

     Best wishes!

Zhou

luo@odu.edu

We understand why you have to add force twice, half and half: the first half before collision and the other after -- you can see that in several papers by Prof. P. Lallemand and myself. This has something to do with "Strang splitting" in finite-difference. There will be a paper by Prof. P. Dellar (Oxford) coming out providing the point.

huadie

Dear Prof. Luo,

Recentely I read  a paper by Ariel Narv´aez el. named "Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann s imulations" which can be found in the attachment. During this paper, four methods relating to how to add the external force are demonstrated, and I believe Method B is the same way as yours in your paper " An evaluation of lattice Boltzmann schemes for porous medium flow simulation ". However, I think there are some contradiction between them.
In your paper, the modified momentum j' = j + rho_0*a*delta_t/2 (or the modified velocity u' = u + a*delta_t/2) is used as the measured velocity field for output, and in the calculation of nonlinear velocity terms of the equilibria of Eq. (5a) for the moments (or equilibria of Eq. (8) for the distributions). Besides, the external force is added in the Lattice Boltzmann Equation as a source term which can be found in Eqn(1) and (2).
However, in the other paper, the method B means the same thing except that the modification of momentum is not needed in the calculation of nonlinear velocity terms of the equilibria terms.
So, I am looking forward to your kind explanation.
Best wishes!

Zhou

huadie

Prof. Luo's paper

luo@odu.edu

I did not read the paper you mentioned thus cannot discuss it. However, one thing I am sure is that when we discuss a numerical method, it requires certain mathematical analysis in order for us to give concrete comments, and what I said previously is based on analysis, but speculation. If you wish to fully understand the method, you need to sit down and do some in-depth analysis.

-- LSL