关于计算理想气体压力的问题

legendpan

不太明白LB里，如果要计算实际的压力，应该将格子尺度的密度转换成实际密度，然后用理想气体状态方程算？还是用LB模型里隐含的密度和压力的关系，最后将LB单位的压力转换成物理空间压力的单位？

luo@odu.edu

Eqn. (2) is incorrect: p = c_s^2 \rho, also, c_s^2 = R T.

legendpan

sorry for mistyping Eqn.(2).
c_s^2 = R T, c_s is a constant, then can temperature T  be changed?
If I need to caculate pressure in physical unit, whether should I get it from Eqn.(1) by temperature in phsical unit or  directly transform  pressure in lattice unit into physical unit?

luo@odu.edu

NO -- the temperature T has to be a constant to the grid spacing is uniform.

So, the temperature T has to be dealt with in a separately (by another equation). This is an inherent limitation of the LBE (so it is NOT a genuine compressible scheme). That is the point I have been talking about and getting no where. ;-}

legendpan

I get it. Do you mean that in Eqn. cs=R*T_1, the temperature T_1 is not the real temperatue. If I caculate temperature separately by another distribution function, I yield the real temperature, T_2. So T_2 has nothing to do with T_1. Beacuse the D2Q9 is a imcompressible model.

luo@odu.edu

Yes, you get that more or less right. You can read the papers by Lallemand and Luo on the analysis of this.

legendpan

Thank you for your suggestion.