Hello, everyone,

I have some problems in the heat transfer problem in LBM. In the steady heat conduction, the temperature field is relation to the thermal conductivity. But in LBM, the heat transfer equation is relation to the parameter that thermal diffusivity minus 0.5. Then the proportion is different, so the result is different. How to explain this problem?

Are you talking about the advection-diffusion type equation

d(phi)/dt+u*grad(phi)=D*grad^2(phi)

that arises form the LBE? If so, canâ€™t you just define D=tau/3-0.5?

Note that the factor 0.5 is due to the low order discretisation (forward Euler) of the discete-velocity Boltzmann equation. If you are not happy with this 0.5 then you can discretise the discete-velocity Boltzmann equation by Crank-Nickolson instead (see, for example, He Shan and Doolen 1998, Lee and Fischer 2006, Asinari 2008, Reis and Dellar 2011 (which is for an advection-(reaction)-diffusion equation)).