constant value in Thermal lattice Boltzmann

dear all
I am working in Phd thesis but i faced with a problem which i couldnt solve. please help me becasue iam really need your attentions,
my question is that:
i consider simple case, periodic flow in channel in 2D. I try to simulate this flow and compare with analytical solution, but i dont know how to compute R(gas constant) and Cv(specific heat at constat value). i consider papers,all of them use these values but no body tells how to compute these values. just I saw one equation: 3RT=1, but i dont know which T i have to use?
really thanks
Ehsan

Hi Ehsan,

Most LBEs deal with isothermal flows and as a result don’t really worry too much about these quantities. In “standard” models, we use a (pseudo) equation of state, P=rhoRT=(rho*c^2)/3, where c=delta_x/delta_t is the ratio of space-step to time-step. I say “pseudo” because since we take c to be a numerical parameter (a scaling velocity), the physical equation of state changes with the scaling used to solve the problem. (Note that R=R_0/M, where R_0 is the universal gas constant and M is the molar mass…but we are interested in numerics, not just physics.)

Instead, we could use “P=rhoRT” directly in our model (ie, the the equilibrium function, and the resulting moment system) so we can adjust RT. If RT>1/3, we have a negative bulk viscosity and the model is unstable. R and T maybe given for a certain gas, so we could then compute the flow with the necessary physical equation of state and acceptable discretisation parameter © for an efficient algorithm. However, I think RT=1/3 is still the most stable. You may want to have a look at this paper http://pre.aps.org/abstract/PRE/v65/i3/e036309

I’m not sure if this was any use to you. For the D2Q9 model, the temperate is constant.

Good luck!

really thanks
but i think i have to clarify something, I am simulating thermal model of lattice boltzmann and i tried to simulate 2-D thermal Poiseulle flow in channel. my refreneces were [1] and [2].but for doing them, i need to know R(gas constant) and Cv(specific heat at constat value) but i dont know how to compute them. and it really mixed me up.
really thanks
best regard
Ehsan

[1] A thermal lattice Boltzmann model for flow with viscous heat dissipation, Hao and el
[2] simulating two_dimensional thermal channel flow by means of a lattice Boltzmann method with new boundary conditions. D’ Orazio and el

Well, the universal gas constant is…well, it is universal; and the molar mass depends on the fluid you are using. Although I have never done it, I suppose this means we can put them directly into the equation of state, together with the temperature found…?? I’m just thinking out aloud now so may be talking rubbish, but if this works then we know that the specific heat ratio for a monatomic gas is 5/3 and we know the specific gas constant (ie R/(molar mass) is c_p-c_v; so in principle you have everything you need. The problem is: is the thermal LB model a good one?!