I am new in LBM and I’ve just started to develop a code for thermal 3D. I wrote a code for D2Q9. In 2D there are several good papers and you can find all equations and all boundary conditions and parameters in them!
For 3D I couldn’t find any! I want to write a 3DQ19 and I used Peng paper [1] but there is nothing about boundary conditions and parameters in a 3D model!
Could you please help me to write BC of a 3DQ19, for a simple rectangular duct; boundary conditions of temperature inlet, constant wall temperature and fully developed.
Any help is greatly appreciated.

[1]Y. Peng, C. Shu, Y.T. Chew
A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity,
Journal of Computational Physics 193 (2003) 260–274

First of all I think that D3Q19 is not sufficient for resolving the moments necessary for the energy equation just as in 2d, D2Q9 is not enough. For 3d the one I think you need is D3Q27.

Given that most equilbrium equations are given in vector form extending to 3d should not be an issue as long as your velocities are composed into x, y and z directions. Also the boundary conditions should just be a logical extension of the 2d conditions doing filling the same function. Do you need anything in specific?

Thanks for your message!
I’ve already written a D3Q19 code for fluid flow part and I got good results!
I wrote a code for D2Q9 before, and for the thermal part I followed the method of D’Orazio ! I got good results for 2D thermal! If you look at D’Orazio paper you see how clear BCs are in her paper! I don’t know how she derived them! I just followed hers!
I don’t know if the BCs for 3D would be like 2D in her paper or not! Constants in equations would be the same or not!
I wrote all subroutine for thermal 3D but boundary condition one! Could you please give me the clear equations for BCs?
Thanks in advance for your help!

D’Orazio A, Succi S,Simulating two-dimensional thermal channel flows by means of a lattice Boltzmann method with new boundary conditions,FUTURE GENERATION COMPUTER SYSTEMS Volume: 20 Issue: 6 Pages: 935-944 Published: AUG 2004

Do you run the channel flow using D3Q19? If so, what boundary conditions do you apply? Zou/He or periodic?

I am using D3Q19 for duct flow, but get in some trouble.

The velocity vectors at every cross section are pointing to +x +y +z direction, while it should’ve pointed to the flow direction as a parabloic-like profile.

I follow the paper ‘Laboratory validation of lattice Boltzmann method for modeling pore-scale flow in granular materials, Computers and Geotechnics 33 (2006), 381-395’, on page 388 the in/out boundary conditions.

I found out the problem and have tried to solve it but still no correct reslts for a week.