# LBM: a good method for my problem ?

Hello,
I have the following problem in a nontrivial 3D geometry (let’s call it a box in the following). In a certain region inside the box a gas is created by evaporation (according to a time-dependent emission rate), then flows through the box and is partially (i.e. with a certain particle sticking probability between 0 and 1) adsorbed when it comes to the walls of the box. Emission stops after a while and in the end all the gas is deposited on the walls. I am interested to find out the final deposition distribution on the box’s surface.
I am tempted to use a mesoscopic technique to study my problem and thought about LBM. I see some potential problems and therefore have the following questions:

1. In the beginning the box is empty, then gas is created and density increases (fast and to a high value in my case), towards the end density decreases again, and in the end the box is empty. Therefore I have different phases with very different Knudsen numbers: very high in the beginning and the end, i.e. a rarified flow, and very low in between. LBM seems good only for the intermediate phase, right? Or can one tune the collision part somehow?
2. The created gas has a Maxwell distribution linked to a certain temperature. How do I set the time scale in LBM? Is my velocity of the same order as the speed of sound in the system, i.e. Mach number around 1? Does LBM work at all in such a situation or what is the maximum possible Mach number?
3. Boundary conditions: I thought to modify the boundary conditions. Create particle distributions in a certain region in the interior where gas is created and modify the reflective boundary to take care of partial adsorption at the box’s wall. From a physical point of view it looks straightforward. Do you have seen any such cases in LBM? Do you expect problems?
4. Is LBM the best method? If not, what would of the following would you suggest (or exclude): discrete velocity method, dissipative particle dynamics, smoothed-particle hydrodynamics, direct simulation Monte Carlo, molecular dynamics, or any hybrid method ?