Hello, guys, I am going to solve a very easy problem of 2-d box with top lid moving,
I got this case from Jonas Latt’s ‘Choice of units in lattice Boltzmann simulations’,
however, I do not know how to treat with the moving wall boundary as the top lid
is, I am really a beginner, can anybody give me some advice? Thank you in advance.

Sorry, I have seen previous posts on this topic and am downloading Succi’s book, Thank you.

I’m not entirely sure which type of boundary condition you are referring to when you speak of a moving wall boundary. If you mean a wall that actually changes its location during the simulation (e.g. the rotor blades of a helicopter or heart valves in a simulation of medical physics), then the answer to your question is tough. Things are easier if, as it seems to be the case, you are referring to the simulation of a lid-driven cavity. In this case the wall is not actually moving, but the fluid on the wall is defined to have a non-zero velocity. There exist different ways to impose a fixed velocity on a straight wall. A few of them are summarized in this review paper.

Thank you, jlatt, I am getting familiar with the boundary treatment following
your paper and Succi’s book, however, I am still wondering how to set
initial value of distribution function. I did do the lid-driven cavity problem.
Thank you again.

simple problems can be initialized with an equilibrium distribution. for more complicated problems, you can use the method shown in this paper: http://www.lbmethod.org/literature:skordos_93