I am using D3Q19 model for simulating a 3D square duct flow. For the rectangular cross section(y and z are along the width and height direction respectively) at the inlet with x being the flow direction, I want to set a inlet velocity bounary condition to satisfy a prescribed flow rate Q. But unfortunately I don’t know how to give the velocity value at each lattice site at the cross section of the inlet. Before I treated 2D and assumed a full developed velocity profile at the inlet, what about the inlet velocity profile in 3D? Of course, other treatments will be OK for me, I just want to satisfy a given inlet flow rate. Anyone has the experience to share with me, i would be much appreciate. Many thanks

If you just want to have a given rate, say Q, then why not do the following:

Compare the total cross section in lattice units, i.e. A = N_y * N_z

Divide Q by A and set the velocity along the x-axis according to v_x = Q / A. The other velocity components are zero.
If you want to introduce a fully developed flow at the inlet (3D Poiseuille flow), then you should have a look at those two papers: paper 1[/url] [url=http://arxiv.org/abs/0812.3242]paper 2

Hi Timm,
Thank you for your advices.
I have used the method just like the first one you proposed. If so, i need to have a long extended regime at the inlet in order that the flow can develop into a full-developed one. For my problem, there will be a significant increase in computing cost.
Haihu

This is not necessarily true. If you are working with a small Reynolds number, the additional tube length is rather short. There is an article dealing with this issue. I am not in my office right now, and I do not know the authors or title by heart. If you are interested, I can have a look at my literature on Monday.
For a Reynolds number smaller than 1, the additional length until the flow is steady is appr. the diameter of the channel.
A more elegant way is the direct implementation of the fully developed velocity.