shockwaves reflecting on outflow boundaries

Lattice Boltzmann Method LBM: Theory
#1

Hi there!
There are some effects that appear in my LBM solver that I don’t understand. Maybe anybody of you knows why this happens…

I’ve implemented a LBM solver and build a testcase with incoming flow at the boundary on one side of the domain. On the inflow boundary I set a fixed velocity u and compute the distribution functions f by setting them to the equilibrium f_eq(u, rho) with unit density (rho = 1).

On the other side of the domain I set the outflow boundary thus, that the outer cells get the values of their neighbors in the direction normal to the boundary (e.g. I got a rectangular domain and set the values on the boundary on the right side to the values of their neighbors left of them).

The rest of the flow field I initialize with zero velocity and with unit density.

Further I set the lattice speed u_lb to 0.02 and the lattice viscosity nu_lb to 0.004 yielding a relaxation time tau of 0.512.

When I start my solver now there appear structures that look like shockwaves and those shockwaves reflect on the boundary…
If I increase the viscosity (say to nu_lb=0.01 --> tau=0.53) the structures are not that strong, but still appear and reflect on the outflow boundary.

Does anybody know why these structures appear? Is it correct that they appear? And if not, what can I do to prevent them?

#2

you know that there exist more precise boundary conditions, don’t you?

the velocity profile of your initial condition is discontinuous at the inlet. this is probably the origin of your acoustic waves. try a smooth initial condition (e.g. constant velocity everywhere).

#3

Hallo adam,

thank you for your answer. It sounds plausible to me… :slight_smile:

I know that there are other boundary conditions. But since this one was easy to understand and implement I used it for my first approach. What boundary condition would you suggest for a setting like the one I described above?