# Initialization for DNS - channel case

Hi all,

I have problem in initialization in channel case using LBM. My LBM channel case is working very well for laminar flow but when i try to change to DNS it is not working. I guess my initialization method for DNS is wrong. Do you have any idea how to overcome this problem?

Regards,
Min

Hello,

It is a bit difficult to give an answer to your problem. I guess that you are trying to solve a turbulent channel flow without any turbulence model. First are you sure you are resolved enough for your problem? If you are too much underresolved then a numerical instability will appear. If you are indeed resolved enough then could you give more details about your simulation setup : resolution, u_max, Re, tau, … What kind of boundary conditions are you using?

Orestis

Let me continue the topic … I have similar problem ie. the turbulent simulation in 2D channel crossection… I would like to find a velocity profile for a flow between two plates… Thus assume 2D channel and D2Q9 BGK model. I do not want introduce any turbulent models since it should be the LBM to verify turbulent models – the DNS (direct numerical simulation)

[A] Is there any fundamental limitation for high Reynolds number flow modeling using LBM ? I haven’t found any except grid resolution.

Assuming that there is no any limitation my simulation is as follow:

Discretization:
Mesh 602 (flow direction) x 602
Time steps: 3.5e+6

Boundary Conditions:
Inlet/Outlet: periodic
Side walls: bounce back
Initial Conditions:
Distributions in are set to have non 0 x-direction velocity. The velocity gives the Re=5000 ca…

Simulation
During simulation the Y -velocity component is beeing relaxed, no forcing terms.

LBM model parametrs
Mesh:
Re=5000
mesh
(Lx x Ly x Lz)~Re^(9/4) ? (Lx x Ly)~Re^(6/4) ? Lx x Ly ~ (353E+3 points)–>ca. 600 x 600 grid
Time resolution ~ dt~dx^2 ? (Nt=350e+3 points)
viscosity: visc=(dt/dx^2)*1/Re : visc=0.000020571
where dt=1/Nt, dx=1/Lx (Nt- lbm time steps, Lx grid points along flow direction)
Mach number E_Ma~dt/dx : E_Ma= 600/3.5e+6=0.026 which is close to the value adviced in  ulb=0.02
fulfilled relation dt~dx^2 

Relaxation Factor:
tau=visc/cs^2+0.5=0.000020571*3+0.5=0.500061714 ? omega=1/tau=1.99975, which is v. close to 2 !!!
Literature:

 Jonass Latt Phd Thesis “Hydrodynamic limit of lattice Boltzmann equation”
Jonas Latt at al. “Numerical Analysis of the Averaged Flow Field in a Turbulent Lattice Boltzmann Simulation” preprint submitted to Elsevier Science, 2004
 Dustin Bespalko, Andrew Pollard, Mesbah Uddin “Direct Numerical Simulation of Fully-Developed Turbulent Channel Flow Using the Lattice Boltzmann Method and Analysis of OpenMP Scalability” , presentation
 Jonass Latt “Choice of units in lattice Boltzmann simulations
” 2008

My questions

[B] Are assumptions/calculation correct ?
[C] Did anyone such simulation and could present even qualitative results ? I wonder how LBM compares with eg. k-epsilon model concerning velocity profiles