Thermal modeling(Adiabatic bounadary condition)

Dear all,
I want to model adiabatic boundary condition on a thermal problem via LBM. I use one model to implement this kind of boundary condition. But my results are instable. what is the most recent update model to implement the adiabatic boundary condition.
Thank you,

You can use adiabatic boundary condition… For the adiabatic boundary condition to find the temperature, second-order finite difference approximation is used. As an example, the two-dimensional square cavity case of the bottom wall
T(i,0) = 4/3* T(i,1) - 1/3* T(i,2)

where is the temperature on the wall; and are the temperatures inside the flow domain near the wall. The method used to find the temperature in the present work also found to be numerically stable.

nanolb, what thermal model and what adiabatic boundary condition are you using? pls give a reference to a paper if you can.

thank you perumal for your help. thank you adam for your notice.
I use guo’s model(passive scalar). dear perumal, i think if we use your method we omit two terms that are introduced in guo’s model.
T^eq i(x_b,t),T^eq i(xf,t)
But as you mension, iuse your method and i found stable solution. but when i implement these two terms, my solutions are unstable.
Thank you
sincerely yours